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Ex vivo machine perfusion (EVMP) is an emerging technique for preserving explanted solid organs with primary application in allogeneic organ transplantation. EVMP has been established as an alternative to the standard of care static-cold preservation, allowing for prolonged preservation and real-time monitoring of organ quality while reducing/preventing ischemia–reperfusion injury. Moreover, it has paved the way to involve expanded criteria donors, e.g., after circulatory death, thus expanding the donor organ pool. Ongoing improvements in EVMP protocols, especially expanding the duration of preservation, paved the way for its broader application, in particular for reconditioning and modification of diseased organs and tumor and infection therapies and regenerative approaches. Moreover, implementing EVMP for in vivo-like preclinical studies improving disease modeling raises significant interest, while providing an ideal interface for bioengineering and genetic manipulation. These approaches can be applied not only in an allogeneic and xenogeneic transplant setting but also in an autologous setting, where patients can be on temporary organ support while the diseased organs are treated ex vivo, followed by reimplantation of the cured organ. This review provides a comprehensive overview of the differences and similarities in abdominal (kidney and liver) and thoracic (lung and heart) EVMP, focusing on the organ-specific components and preservation techniques, specifically on the composition of perfusion solutions and their supplements and perfusion temperatures and flow conditions. Novel treatment opportunities beyond organ transplantation and limitations of abdominal and thoracic EVMP are delineated to identify complementary interdisciplinary approaches for the application and development of this technique.

(1) Background: Implant-associated bacterial infections are usually hard to treat conservatively due to the resistance and tolerance of the pathogens to conventional antimicrobial therapy. Bacterial colonization of vascular grafts may lead to life-threatening conditions such as sepsis. The objective of this study is to evaluate whether conventional antibiotics and bacteriophages can reliably prevent the bacterial colonization of vascular grafts. (2) Methods: Gram-positive and Gram-negative bacterial infections were simulated on samples of woven PET gelatin-impregnated grafts using Staphylococcus aureus and Escherichia coli strains, respectively. The ability to prevent colonization was evaluated for a mixture of broad-spectrum antibiotics, for strictly lytic species-specific bacteriophage strains, and for a combination of both. All the antimicrobial agents were conventionally tested in order to prove the sensitivity of the used bacterial strains. Furthermore, the substances were used in a liquid form or in combination with a fibrin glue. (3) Results: Despite their strictly lytic nature, the application of bacteriophages alone was not enough to protect the graft samples from both bacteria. The singular application of antibiotics, both with and without fibrin glue, showed a protective effect against S. aureus (0 CFU/cm2), but was not sufficient against E. coli without fibrin glue (M = 7.18 × 104 CFU/cm2). In contrast, the application of a combination of antibiotics and phages showed complete eradication of both bacteria after a single inoculation. The fibrin glue hydrogel provided an increased protection against repetitive exposure to S. aureus (p = 0.05). (4) Conclusions: The application of antibacterial combinations of antibiotics and bacteriophages is an effective approach to the prevention of bacteria-induced vascular graft infections in clinical settings.

Various elements of the Earth system have the potential to undergo critical transitions to a radically different state, under sustained changes to climate forcing. The Atlantic meridional overturning circulation (AMOC) is of particular importance for North Atlantic heat transport and is thought to be potentially at risk of passing such a tipping point (TP). In climate models, the location and likelihood of such TPs depends on model parameters that may be poorly known. Reducing this parametric uncertainty is important to understand the likelihood of tipping behaviour. In this letter, we develop estimates for parametric uncertainty in a simple model of AMOC tipping, using a Bayesian inversion technique. When applied using synthetic (‘perfect model’) salinity timeseries data, the technique drastically reduces the uncertainty in model parameters, compared to prior estimates derived from previous literature, resulting in tighter constraints on the AMOC TPs. To visualise the impact of parametric uncertainty on TPs, we extend classical tipping diagrams by showing probabilistic bifurcation curves according to the inferred distribution of the model parameter, allowing the uncertain locations of TPs along the probabilistic bifurcation curves to be highlighted. Our results show that suitable palaeo-proxy timeseries may contain enough information to assess the likely position of AMOC (and potentially other Earth system) TPs, even in cases where no tipping occurred during the period of the proxy data.

In this paper, we focus on the influence of heterogeneity and stochasticity of the population on thedynamical structure of a basic susceptible-infected-susceptible (SIS) model. Firstwe prove that, upon a suitable mathematical reformulation of the basic reproduction number, thehomogeneous system and the heterogeneous system exhibit a completely analogous globalbehaviour. Then we consider noise terms to incorporate the fluctuation effects and therandom import of the disease into the population and analyse the influence of heterogeneityon warning signs for critical transitions (or tipping points). This theory shows that one maybe able to anticipate whether a bifurcation point is close before it happens. We use numericalsimulations of a stochastic fast-slow heterogeneous population SIS model and show various aspectsof heterogeneity have crucial influences on the scaling laws that are used as early-warningsigns for the homogeneous system. Thus, although the basic structural qualitative dynamicalproperties are the same for both systems, the quantitative features for epidemic predictionare expected to change and care has to be taken to interpret potential warning signs for diseaseoutbreaks correctly.

(1) Objective: Bacterial resistance to conventional antibiotic therapy is an increasingly significant worldwide challenge to human health. The objective is to evaluate whether bacteriophage therapy could complement or be a viable alternative to conventional antibiotic therapy in critical cases of bacterial infection related to cardiothoracic surgery. (2) Methods: Since September 2015, eight patients with multi-drug resistant or especially recalcitrant Staphylococcus aureus, Enterococcus faecium, Pseudomonas aeruginosa, Klebsiella pneumoniae, and Escherichia coli infections were treated with bacteriophage preparations as a therapy of last resort according to Article 37 of the Declaration of Helsinki. Patients had infections associated with immunosuppression after organ transplantation or had infections of vascular grafts, implanted medical devices, and surgical wounds. Individualized phage preparations were administered locally, orally, or via inhalation for different durations depending on the case. All patients remained on conventional antibiotics during bacteriophage treatment. (3) Results: Patients ranged in age from 13 to 66 years old (average 48.5 ± 16.7) with seven males and one female. Eradication of target bacteria was reached in seven of eight patients. No severe adverse side effects were observed. (4) Conclusions: Phage therapy can effectively treat bacterial infections related to cardiothoracic surgery when conventional antibiotic therapy fails.

In this article we report on a novel way to incorporate complex network structure into the analysis of interacting particle systems. More precisely, it is well-known that in well-mixed/homogeneous/all-to-all-coupled systems, one may derive mean-field limit equations such as Vlasov–Fokker–Planck equations (VFPEs). A mesoscopic VFPE describes the probability of finding a single vertex/particle in a certain state, forming a bridge between microscopic statistical physics and macroscopic fluid-type approximations. One major obstacle in this framework is to incorporate complex network structures into limiting equations. In many cases, only heuristic approximations exist, or the limits rely on particular classes of integral operators. In this paper, we notice that there is a much more elegant, and profoundly more general, way available due to recent progress in the theory of graph limits. In particular, we show how one may easily enter complex network dynamics via graphops (graph operators) into VFPEs.

Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley's results and prove that the GSPT technique of Fenichel Normal Form can be used to simplify the application of Conley index techniques even further. We also hope that our results provide a better bridge between the different fields. Furthermore we show how to interpret Conley's conditions in terms of averaging. The result are illustrated by the two-dimensional van der Pol equation and by a three-dimensional Morris-Lecar model.

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system's tendency to recover more slowly from a perturbation the closer it gets to the transition--a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws. Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures.

Many science phenomena are modelled as interacting particle systems (IPS) coupled on static networks. In reality, network connections are far more dynamic. Connections among individuals receive feedback from nearby individuals and make changes to better adapt to the world. Hence, it is reasonable to model myriad real-world phenomena as co-evolutionary (or adaptive) networks. These networks are used in different areas including telecommunication, neuroscience, computer science, biochemistry, social science, as well as physics, where Kuramoto-type networks have been widely used to model interaction among a set of oscillators. In this paper, we propose a rigorous formulation for limits of a sequence of co-evolutionary Kuramoto oscillators coupled on heterogeneous co-evolutionary networks, which receive both positive and negative feedback from the dynamics of the oscillators on the networks. We show under mild conditions, the mean field limit (MFL) of the co-evolutionary network exists and the sequence of co-evolutionary Kuramoto networks converges to this MFL. Such MFL is described by solutions of a generalised Vlasov equation. We treat the graph limits as signed graph measures, motivated by the recent work in [Kuehn, Xu. Vlasov equations on digraph measures, JDE, 339 (2022), 261–349]. In comparison to the recently emerging works on MFLs of IPS coupled on non-co-evolutionary networks (i.e., static networks or time-dependent networks independent of the dynamics of the IPS), our work seems the first to rigorously address the MFL of a co-evolutionary network model. The approach is based on our formulation of a generalisation of the co-evolutionary network as a hybrid system of ODEs and measure differential equations parametrised by a vertex variable, together with an analogue of the variation of parameters formula, as well as the generalised Neunzert’s in-cell-particle method developed in [Kuehn, Xu. Vlasov equations on digraph measures, JDE, 339 (2022), 261–349].

In this work, we study early warning signs for stochastic partial differential equations (SPDEs), where the linearisation around a steady state is characterised by continuous spectrum. The studied warning sign takes the form of qualitative changes in the variance as a deterministic bifurcation threshold is approached via parameter variation. Specifically, we focus on the scaling law of the variance near the transition. Since we are dealing here, in contrast to previous studies, with the case of continuous spectrum and quantitative scaling laws, it is natural to start with linearisations of the drift operator that are multiplication operators defined by analytic functions. For a one-dimensional spatial domain, we obtain precise rates of divergence. In the case of the two- and three-dimensional domains, an upper bound to the rate of the early warning sign is proven. These results are cross-validated by numerical simulations. Our theory can be generically useful for several applications, where stochastic and spatial aspects are important in combination with continuous spectrum bifurcations.

We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we incorporate the recently developed graph limit theory of graphops into the limiting McKean–Vlasov equations. Global stability of the splay steady state is proven via a generalised entropy method, leading to explicit graph structure-dependent decay rates. We highlight the robustness of the entropy approach by extending the results to the closely related Sakaguchi–Kuramoto model with intrinsic frequency distributions. We also present central examples of random graphs, such as power law graphs and the spherical graphop, and analyse the limitations of the applied methodology.