综合性期刊最新文献

The flow of cerebrospinal fluid (CSF) through the perivascular spaces (PVSs) and interstitial fluid (ISF) in the extracellular space (ECS) is important for brain waste removal and drug delivery. The circulation of this flow is often called the glymphatic system. We build on an existing hydraulic network model of steady flow in this system to enable the study of time-dependent flows, allowing the modelling of the processes of tracer injection and drug delivery in the glymphatic network. Using flow rates from the steady-state model and the method of Laplace transforms, we solve this time-dependent advection-diffusion equation for the network semi-analytically and show that the solution closely matches numerical simulations. We find that a particular value of the endfoot gap cavity fraction maximizes solute perfusion. Furthermore, we find that a smaller gap fraction around PVS segments at the brain surface and a larger gap fraction around deeper PVS segments produce more uniform perfusion, which is consistent with a previous study (Wang et al. 2021 Glia69, 715-728 (doi:10.1002/glia.23923)). We also observe that greater permeability of the ECS improves perfusion, and that tracers with lower diffusivity exhibit enhanced perfusion.

Individual heterogeneity, in number of parasites, size, etc., interacts critically with population dynamics. We tease this out in a model case study of microparasite load with empirically supported assumptions to investigate how variance in load interacts with population dynamics, We show how the mean and variance of load vary throughout an epidemic. Further, we show how mean and variance have mutual negative feedbacks on each other mediated by high death rates at high loads. Helpfully, we find that mean and variance provide information into underlying processes as well. Population trends in the mean and variance reveal underlying trends in within-host processes, e.g. differentiating host evolution of defence that manifests as tolerance, constitutive resistance, inducible resistance or acquired resistance. Our findings apply to many microparasites, including fungal pathogens which show large variance in infection load. As a case study, we consider endangered frog populations recovering from fungal epidemics and find that the mean and variance guide management actions. Lastly, we demonstrate the impact of load variance on host fitness, pathogen fitness and host population suppression. Our results demonstrate the importance of trait heterogeneity and the insights available from relatively simple models, both for microparasite load and possibly other traits.

This paper presents the first application of the Modified Extended Direct Algebraic (MEDA) method to the (2+1)-dimensional Wazwaz-Kaur-Boussinesq equation, a model governing wave dynamics in shallow waters. The approach successfully uncovers previously unreported classes of exact solutions, including combo dark-singular solitons and Jacobi elliptic function solutions. The spectrum of obtained solutions-which also encompasses bright, dark, and singular solitons, as well as hyperbolic, periodic, exponential, and rational functions-reveals rich and complex soliton dynamics. A comprehensive stability analysis confirms the robustness of these solutions under perturbation. These results significantly advance the understanding of wave propagation in nonlinear systems, providing valuable insights for applications in fluid dynamics, nonlinear optics, and plasma physics, while demonstrating the efficacy of the MEDA method for tackling complex nonlinear evolution equations.