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Background: Muscle pain and stiffness are strictly interconnected. Injuries frequently occur during sport activities, causing muscle pain, with or without stiffness, and require effective as well as fast-acting treatments. Topical products can be ideal for the treatment of such physical alterations as they are convenient and simple to use. In this study, it was investigated the application of a novel topical formulation, EGYFIL™, for the treatment of pain and stiffness due to muscle contracture, trauma, and/or overtraining. The lotion is composed of hyaluronic acid, a well-known ingredient for the pain alleviation, mixed with skin conditioning SH-Polypeptide-6 and SH-Oligopeptide-1, embedded in it., Methods: Twenty-six patients with pain and/or stiffness were enrolled. After a screening visit (Time 0, t0), patients were treated for the first time with the IP. The treatment consisted of topical application of the pain lotion. Level of pain and stiffness were measured with Numerical Rating Scale (NRS). Patients' pain and/or stiffness were evaluated at t0 (prior to using the product), after three hours (t1), and after three days (t2) of treatment. Participants were free to apply and re-apply the product ad libitum over the course of the study period (3 days). Potential adverse events (AE) and tolerance were evaluated during each visit., Results: There was a 22% decrease in pain in the first three hours (p < 0.001), followed by an additional 20% decrease after three days (p=0.0873). Overall, there was a 42% decrease in pain over the three days of the study (p =0.001). Furthermore, a 24% reduction in stiffness in the first three hours (p=0.025) and a 38% decrease in stiffness over three days (p < 0.001) were observed. Reduction in pain and stiffness were neither age, nor sex dependent. No adverse effects were reported during the study., Conclusion: EGYFIL™ is safe and seems to reduce pain and stiffness in patients during the 3 days of treatment, already after 3 h from the first application., Trial Registration: ClinicalTrials.gov ID: NCT05711953. This trial was registered on 03/02/2023., (© 2023. BioMed Central Ltd., part of Springer Nature.)

In thermoelastic wave attenuation, such as that caused by heterogeneities much smaller than the wavelength, e.g., Savage theory of spherical pores, the shape of the relaxation peak differs from that of the Zener (or standard linear solid) mechanical model. In these effective homogeneous media, the anelastic behavior is better represented by a stress-strain relation based on fractional derivatives; particularly, P- and S-wave dispersion and attenuation is well described by a Cole-Cole equation. We propose a time-domain algorithm for wave propagation based on the Grünwald-Letnikov numerical derivative and the Fourier pseudospectral method to compute the spatial derivatives. As an example, we consider Savage theory and verify the algorithm by comparison with the analytical solution in homogeneous media based on the frequency-domain Green function. Moreover, we illustrate the modeling performance with wave propagation in a two half-space medium where one section is lossless and the other is a Cole-Cole medium. This apparently simple example, which does not have an analytical solution, shows the complexity of the wavefield that characterizes a single flat interface.

P-wave conversion to slow diffusion (Biot) modes at mesoscopic (small-scale) inhomogeneities in porous media is believed to be the most important attenuation mechanisms at seismic frequencies. This study considers three periodic thin layers saturated with gas, oil, and water, respectively, a realistic scenario in hydrocarbon reservoirs, and perform finite-element numerical simulations to obtain the wave velocities and quality factors along the direction perpendicular to layering. The results are validated by comparison to the Norris-Cavallini analytical solution, constituting a cross-check for both theory and numerical simulations. The approach is not restricted to partial saturation but also applies to relevant properties in reservoir geophysics, such as porosity and permeability heterogeneities. This paper considers two cases, namely, the same rock skeleton and different fluids, and the same fluid and different dry-rock properties. Unlike the two-layer case (two fluids), the results show two relaxation peaks and the agreement between numerical and analytical solutions is excellent.

The acoustic behavior of porous media can be simulated more realistically using a stress-strain relation based on the Cole-Cole model. In particular, seismic velocity dispersion and attenuation in porous rocks is well described by mesoscopic-loss models. Using the Zener model to simulate wave propagation is a rough approximation, while the Cole-Cole model provides an optimal description of the physics. Here, a time-domain algorithm is proposed based on the Grünwald-Letnikov numerical approximation of the fractional derivative involved in the time-domain representation of the Cole-Cole model, while the spatial derivatives are computed with the Fourier pseudospectral method. The numerical solution is successfully tested against an analytical solution. The methodology is applied to a model of saline aquifer, where carbon dioxide (CO 2 ) is injected. To follow the migration of the gas and detect possible leakages, seismic monitoring surveys should be carried out periodically. To this aim, the sensitivity of the seismic method must be carefully assessed for the specific case. The simulated test considers a possible leakage in the overburden, above the caprock, where the sandstone is partially saturated with gas and brine. The numerical examples illustrate the implementation of the theory.