Purpose: Given the high incidence of patellofemoral pain syndrome (PFPS) in runners, this study aimed to investigate the immediate effect of shoes with different minimalist indices (MI) on the mechanical loads of the patellofemoral joint. Methods: Fifteen healthy male rearfoot strike runners were recruited to complete overground running trials at 3.33 m/s (±5%) in two running shoe conditions (MI = 26% versus MI = 86%). The amount of ten Vicon infrared cameras (100 Hz) and two Kistler force plates (1000 Hz) were used to collect kinematic and ground reaction force (GRF) data simultaneously. Quadriceps strength, patellofemoral contact force, patellofemoral contact area, and patellofemoral contact stress were calculated. Results: No significant differences were observed in the impact force and the second peak of the vertical GRF between the two shoe conditions. Compared to wearing low-MI shoes, wearing high-MI shoes showed that the maximum flexion angle of the knee, the contact area of patellofemoral joint and the peak knee extension moment reduced significantly (p < 0.01), and the peak patellofemoral contact force and stress decreased significantly (p < 0.05). Conclusion: These findings suggest that wearing high-MI shoes significantly decreases the patellofemoral contact force and patellofemoral joint stress by reducing the moment of knee extension, thus effectively reducing the load of the patellofemoral joint during the stance phase of running and potentially lowering the risk of PFPS.
Nowadays, compression garments (CGs) are widely used in winter racing sports, such as speed skating, short-track speed skating, alpine skiing, and crosscountry skiing. However, the effect of wearing CGs on athletic performance in these specific sports is still not fully examined. Thus, the aim of this narrative review is to summarize the research and application of CGs in winter racing sports and to discuss how the CGs help athletes improve their performance in an integrative manner (i.e., physiology, aerodynamics, and biomechanics). A total of 18 experimental studies dedicated to CGs in winter racing sports were identified from the peer-review scientific literature. The main findings are as follows. (1) Currently, CG studies have mainly focused on drag reduction, metabolism, muscle function, strength performance, and fatigue recovery. (2) The results of most studies conducted in wind tunnels showed that, for cylindrical structures similar to the human body, clothing with rough surfaces can reduce air drag. Notably, the effect of CGs on drag reduction in real competition has not been fully explored in the literature. (3) Compression can reduce muscle vibrations at high impact and help athletes control the center of pressure movement, a function that is important for alpine skiing. Future studies are needed to improve current understanding of the effects of compression clothing microstructure on drag reduction and their stretching in different parts of the body. Furthermore, the design of experimental protocol must be consistent with those during the competition, thus providing a full discussion on energy metabolism, fatigue, and recovery affected by CGs.
Full-waveform inversion (FWI) includes migration and tomography modes. The tomographic component of the gradient from reflection data is usually much weaker than the migration component. To use the tomography mode to fix background velocity errors, it is necessary to extract the tomographic component from the gradient. Otherwise, the inversion will be dominated by the migration mode. We have developed a method based on nonstationary smoothing to extract the tomographic component from the raw gradient. By analyzing the characteristics of the scattering angle filtering, the wavenumber of the tomographic component at a given frequency is seen to be smaller than that of the migration component. Therefore, low-wavenumber-pass filtering can be applied to extract the tomographic component. The low-wavenumber-pass smoothing filters are designed with Gaussian filters that are determined by the frequency of inversion, the model velocity, and the minimum scattering angle. Thus, this filtering is nonstationary smoothing in the space domain. Because this filtering is carried out frequency by frequency, it works naturally and efficiently for FWI based on frequency-domain modeling. Furthermore, because the maximum opening angle of the reflections in a typical acquisition geometry is much smaller than the minimum scattering angle for the tomographic component, which is generally set at 160°, there is a relatively large gap between the wavenumbers of the tomographic and migration components. In other words, the nonstationary smoothing can be applied once to a group of frequencies for time-domain FWI without leaking the migration component into the tomographic component. Analyses and numerical tests indicate that two frequency groups are generally sufficient to extract the tomographic component for the typical frequency range of time-domain FWI. The numerical tests also demonstrate that the nonstationary smoothing method is effective and efficient at extracting the tomographic component for reflection waveform inversion.
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