Meniscal T1rho and T2 measured with 3.0T MRI increases directly after running a marathon

PURPOSE: To prospectively evaluate changes in T1rho and T2 relaxation time in the meniscus using 3.0 T MRI in asymptomatic knees of marathon runners and to compare these findings with those of age-matched healthy subjects. MATERIAL AND METHODS: Thirteen marathon runners underwent 3.0 T MRI including T1rho and T2 mapping sequences before, 48-72 h after, and 3 months after competition. Ten controls were examined at baseline and after 3 months. All images were analyzed by two musculoskeletal radiologists identifying and grading cartilage, meniscal, ligamentous. and other knee abnormalities with WORMS scores. Meniscal segmentation was performed to generate T1rho and T2 maps in six compartments. RESULTS: No differences in morphological knee abnormalities were found before and after the marathon. However, all marathon runners showed a significant increase in T1rho and T2 values after competition in all meniscus compartments (p < 0.0001), which may indicate changes in the biochemical composition of meniscal tissue. While T2 values decreased after 3 months T1rho values remained at a high level, indicating persisting changes in the meniscal matrix composition after a marathon. CONCLUSION: T2 values in menisci have the potential to be used as biomarkers for identifying reversible meniscus matrix changes indicating potential tissue damage. T1rho values need further study, but may be a valuable marker for diagnosing early, degenerative changes in the menisci following exercise

Mathematical surprises and Dirac's formalism in quantum mechanics

By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space formulation, we devote the second part of our paper to the latter approach: we discuss the problems and shortcomings of this formalism as well as those of the bra and ket notation introduced by Dirac in this context. In conclusion, we indicate how all of these problems can be solved or at least avoided.Comment: Largely extended and reorganized version, with new title and abstract and with 2 figures added (published version), 54 page