Interplay between particle trapping and heterogeneity in anomalous diffusion

Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid diffusion model that merges a position-dependent diffusion coefficient with the trapping mechanism of the comb model. We derive exact solutions for position distributions and mean squared displacements, validated through simulations of Langevin equations. Our model shows that the trapping mechanism attenuates the impact of media heterogeneity. Superdiffusion occurs when the position-dependent coefficient increases superlinearly, while subdiffusion occurs for sublinear and inverse power-law relations. This nontrivial interplay between heterogeneity and state-independent mechanisms also leads to anomalous yet Brownian and non-Brownian yet Gaussian regimes. These findings emphasize the need for cautious interpretations of experiments and highlight the limitations of relying solely on mean squared displacements or position distributions for diffusion characterization.Comment: 13 two-column pages, 6 figures; accepted for publication in Communications Physic

Endothelial Progenitor Cells Predict Cardiovascular Events after Atherothrombotic Stroke and Acute Myocardial Infarction. A PROCELL Substudy.

Introduction: The aim of this study was to determine prognostic factors for the risk of new vascular events during the first 6 months after acute myocardial infarction (AMI) or atherothrombotic stroke (AS). We were interested in the prognostic role of endothelial progenitor cells (EPC) and circulating endothelial cells (CEC). Methods: Between February 2009 and July 2012, 100 AMI and 50 AS patients were consecutively studied in three Spanish centres. Patients with previously documented coronary artery disease or ischemic strokes were excluded. Samples were collected within 24h of onset of symptoms. EPC and CEC were studied using flow cytometry and categorized by quartiles. Patients were followed for up to 6 months. NVE was defined as new acute coronary syndrome, transient ischemic attack (TIA), stroke, or any hospitalization or death from cardiovascular causes. The variables included in the analysis included: vascular risk factors, carotid intima-media thickness (IMT), atherosclerotic burden and basal EPC and CEC count. Multivariate survival analysis was performed using Cox regression analysis. Results: During follow-up, 19 patients (12.66%) had a new vascular event (5 strokes; 3 TIAs; 4 AMI; 6 hospitalizations; 1 death). Vascular events were associated with age (P = 0.039), carotid IMT≥0.9 (P = 0.044), and EPC count (P = 0.041) in the univariate analysis. Multivariate Cox regression analysis showed an independent association with EPC in the lowest quartile (HR: 10.33, 95%CI (1.22-87.34), P = 0.032] and IMT≥0.9 [HR: 4.12, 95%CI (1.21-13.95), P = 0.023]. Conclusions: Basal EPC and IMT≥0.9 can predict future vascular events in patients with AMI and AS, but CEC count does not affect cardiovascular risk

The Role of Fractional Time-Derivative Operators on Anomalous Diffusion

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes

Interplay between particle trapping and heterogeneity in anomalous diffusion

Abstract Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction with position-dependent diffusion, potentially leading to erroneous conclusions. Here, we introduce a hybrid diffusion model that merges a position-dependent diffusion coefficient with the trapping mechanism of the comb model. We derive exact solutions for position distributions and mean squared displacements, validated through simulations of Langevin equations. Our model shows that the trapping mechanism attenuates the impact of media heterogeneity. Superdiffusion occurs when the position-dependent coefficient increases superlinearly, while subdiffusion occurs for sublinear and inverse power-law relations. This nontrivial interplay between heterogeneity and state-independent mechanisms also leads to anomalous yet Brownian, and non-Brownian yet Gaussian regimes. These findings emphasize the need for cautious interpretations of experiments and highlight the limitations of relying solely on mean squared displacements or position distributions for diffusion characterization

Pharmacological approaches to acute ischaemic stroke: reperfusion certainly, neuroprotection possibly

Stroke is a major cause of both death and disability. However, there are no pharmacological treatments used in most countries other than recombinant tissue plasminogen activator, a thrombolytic, and this is only used in about 4% of patients presenting after an acute ischaemic stroke. One novel thrombolytic (desmoteplase) has just been reported to have failed in a Phase IIb/III trial, but other thrombolytics and reperfusion agents remain in development. The picture with neuroprotectant agents, that is compounds that act to preserve neurones following an acute cerebral ischaemic insult, is even more bleak. Despite the development of over 1000 compounds, many proving effective in animal models of stroke, none has demonstrated efficacy in patients in the over 100 clinical trials conducted. This includes NXY-059, which was developed in accordance with the guidelines proposed by an academic-industry roundtable group (STAIR). This review examines the available data on compounds currently in development. It also proposes that the failure of translation between efficacy in preclinical models and patients is likely to terminate most current neuroprotective drug development. It is suggested that animal models must be made more representative of the patient condition (with other co-morbid conditions) and suggests that since stroke is primarily a cardiovascular disease with a neurological outcome, more research on the neurovascular unit would be valuable. New approaches on neuroinflammation, neurorestoration and neurorepair are also likely to gain prominence in the search for new drugs to treat this major clinical problem