Some results on holomorphic generalized functions

In this note, we present three independent results within generalized complex analysis (in the Colombeau sense). The first of them deals with non-removable singularities; we construct a generalized function u on an open subset Omega of C(n), which is not a holomorphic generalized function on Omega but it is a holomorphic generalized function on Omega\S, where S is a hypersurface contained in Omega. The second result shows the existence of a holomorphic generalized function with prescribed values in the zero-set of a classical holomorphic function. The last result states the existence of a compactly supported solution to the (partial derivative) over bar operator.

The relationship between prevalent medial meniscal intrasubstance signal changes and incident medial meniscal tears in women over a 1-year period assessed with 3.0 T MRI

Objective Intrasubstance meniscal signal changes not reaching the articular surface on fast spin echo (FSE) sequences are considered to represent mucoid degeneration on MRI. The aim of this study was to evaluate the association of prevalent intrasubstance signal changes with incident tears of the medial meniscus detected on 3.0 T MRI over a 1-year period. Materials and methods A total of 161 women aged a parts per thousand yen40 years participated in a longitudinal 1-year observational study of knee osteoarthritis. MRI (3.0 T) was performed at baseline and 12-month follow-up. The anterior horn, body, and posterior horn of the medial meniscus were scored by two experienced musculoskeletal radiologists using the Boston-Leeds Osteoarthritis Knee Score (BLOKS) system. Four grades were used to describe the meniscal morphology: grade 0 (normal), grade 1 (intrasubstance signal changes not reaching the articular surface), grade 2 (single tears), and grade 3 (complex tears and maceration). Fisher`s exact test and the Cochran-Armitage trend test were performed to evaluate whether baseline intrasubstance signal changes (grade 1) predict incident meniscal tears/maceration (grades 2 and/or 3) in the same subregion of the medial meniscus, when compared to subregions without pathology as the reference group (grade 0). Results Medial meniscal intrasubstance signal changes at baseline did not predict tears at follow-up when evaluating the anterior and posterior horns (left-sided p-values 0.06 and 0.59, respectively). No incident tears were detected in the body. Conclusion We could not demonstrate an association between prevalent medial meniscal intrasubstance signal changes with incident tears over a 1-year period.

The association of prevalent medial meniscal pathology with cartilage loss in the medial tibiofemoral compartment over a 2-year period

Objective: To investigate the association of different types of magnetic resonance imaging (MRI)-detected medial meniscal pathology with subregional cartilage loss in the medial tibiofemoral compartment. Methods: A total of 152 women aged >= 40 years, with and without knee osteoarthritis (OA) were included in a longitudinal 24-month observational study. Spoiled gradient recalled acquisitions at steady state (SPGR) and T2-weighted fat-suppressed MRI sequences were acquired. Medial meniscal status of the anterior horn (AH), body, and posterior horn (PH) was graded at baseline: 0 (normal), 1 (intrasubstance meniscal signal changes), 2 (single tears), and 3 (complex tears/maceration). Cartilage segmentation was performed at baseline and 24-month follow-up in various tibiofemoral subregions using computation software. Multiple linear regression models were applied for the analysis with cartilage loss as the outcome. In a first model, the results were adjusted for age and body mass index (BMI). In a second model, the results were adjusted for age, BMI and medial meniscal extrusion. Results: After adjusting for age, BMI, and medial meniscal extrusion, cartilage loss in the total medial tibia (MT) (0.04 mm, P=0.04) and the external medial tibia (eMT) (0.068 mm, P=0.04) increased significantly for compartments with grade 3 lesions. Cartilage loss in the total central medial femoral condyle (cMF) (0.071 mm, P=0.03) also increased significantly for compartments with grade 2 lesions. Cartilage loss at the eMT was significantly related to tears of the PH (0.074 mm; P=0.03). Cartilage loss was not significantly increased for compartments with grade 1 lesions. Conclusion: The protective function of the meniscus appears to be preserved in the presence of intrasubstance meniscal signal changes. Prevalent single tears and meniscal maceration were found to be associated with increased cartilage loss in the same compartment, especially at the PH. (C) 2009 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.