Stability of synchronization in simplicial complexes.

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

Analysis of resorbable mesh implants in short-term human muscular fascia cultures: a pilot study.

PURPOSE: Alteration in fascial tissue collagen composition represents a key factor in hernia etiology and recurrence. Both resorbable and non-resorbable meshes for hernia repair are currently used in the surgical setting. However, no study has investigated so far the role of different implant materials on collagen deposition and tissue remodeling in human fascia. The aim of the present study was to develop a novel ex vivo model of human soft tissue repair mesh implant, and to test its suitability to investigate the effects of different materials on tissue remodeling and collagen composition. METHODS: Resorbable poly-4-hydroxybutyrate and non-resorbable polypropylene mesh implants were embedded in human abdominal fascia samples, mimicking common surgical procedures. Calcein-AM/Propidium Iodide vital staining was used to assess tissue vitality. Tissue morphology was evaluated using Mallory trichrome and hematoxylin and eosin staining. Collagen type I and III expression was determined through immunostaining semi-quantification by color deconvolution. All analyses were performed after 54 days of culture. RESULTS: The established ex vivo model showed good viability at 54 days of culture, confirming both culture method feasibility and implants biocompatibility. Both mesh implants induced a disorganization of collagen fibers pattern. A statistically significantly higher collagen I/III ratio was detected in fascial tissue samples cultured with resorbable implants compared to either non-resorbable implants or meshes-free controls. CONCLUSION: We developed a novel ex vivo model and provided evidence that resorbable polyhydroxybutyrate meshes display better biomechanical properties suitable for proper restoration in surgical hernia repair.

A stochastic reaction scheme for drug/metabolite interaction.

We present a simplified stochastic model to investigate the mechanisms of action of tramadol, a centrally acting analgesic, used for treating pain. The model accounts for the process of metabolization through the cytochrome CYP2D6 and the interactions between molecules and target receptors. The proposed formulation is stochastic in nature and allows to speculate on the role of finite-size fluctuations. Analytically, the master equation, governing the process under scrutiny, is derived and studied in the mean-field limit. The analysis of the associated asymptotic behavior proves interesting for its potential medical implications. The analysis of fluctuations is carried on via the van Kampen expansion. Numerical simulations are also performed to confirm the adequacy of our theoretical prediction.

Modelling the pharmacokinetics of tramadol: on the difference between CYP2D6 extensive and poor metabolizers.

In this work we propose a mathematical model for the kinetics of tramadol, a synthetic opioid commonly used for treating moderate to severe pain. This novel theoretical framework could result in an objective criterion on how to adjust the assigned dose, depending on the genetic polymorphisms of CYP2D6. The model describes the coupled dynamics of tramadol and the metabolite O-desmethyltramadol. The effect of diffusion of the drug in the blood is here accounted for and we further hypothesize the existence of a time delay in the process of chemical translation from tramadol into metabolites. The system of coupled differential equations is solved numerically and the free parameters adjusted so to interpolate the experimental time series for the intravenous injection setting. Theoretical curves are shown to reproduce correctly the experimental profiles obtained from clinical trials. This enables in turn to extract an estimate of the metabolization rate. A difference in metabolization rate between CYP2D6 poor and extensive metabolizers is also found, and the stereoselectivity in the O-demethylation of tramadol highlighted. Our results allow one to quantify the dose of (+)-tramadol (resp. (-)-tramadol) administered to poor or extensive metabolizers, if the same effect is sought. The latter is here quantified through the blood concentration of (+)-metabolites (resp. (-)-metabolites).