Stochastic effects on the dynamics of an epidemic due to population subdivision

Using a stochastic Susceptible-Infected-Removed (SIR) meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a population into mutually independent sub-populations. We show that subdivision activates two stochastic effects---extinction and desynchronization---diminishing the overall impact of the outbreak, even when the total population has already left the stochastic regime and the basic reproduction number is not altered by the subdivision. Both effects are quantitatively captured by our theoretical estimates, allowing us to determine their individual contributions to the observed reduction of the peak of the epidemic.Comment: A proposal for a containment/exit strategy in response to the COVID-19 pandemic. Note the change in title from the original (2020/3/19) version "Containment strategy for an epidemic based on fluctuations in the SIR model

Negative Curvature Boundaries as Wave Emitting Sites for the Control of Biological Excitable Media

Understanding the interaction of electric fields with the complex anatomy of biological excitable media is key to optimizing control strategies for spatiotemporal dynamics in those systems. On the basis of a bidomain description, we provide a unified theory for the electric-field-induced depolarization of the substrate near curved boundaries of generalized shapes, resulting in the localized recruitment of control sites. Our findings are confirmed in experiments on cardiomyocyte cell cultures and supported by two-dimensional numerical simulations on a cross section of a rabbit ventricle.peerReviewe

Dataset for: Complex restitution behavior and reentry in a cardiac tissue model for neonatal mice

Spatio-temporal dynamics in cardiac tissue emerging from the coupling of individual cardiomyocytes underlie the heart’s normal rhythm as well as undesired and possibly life-threatening arrhythmias. While single cells and their transmembrane currents have been studied extensively, systematically investigating spatio-temporal dynamics is complicated by the non-trivial relationship between single-cell and emergent tissue properties. Mathematical models have been employed to bridge this gap and contribute to a deepened understanding of the onset, development and termination of arrhythmias. However, no such tissue-level model currently exists for neonatal mice. Here, we build on a recent single-cell model of neonatal mouse cardiomyocytes by Wang & Sobie (40) to predict properties that are commonly used to gauge arrhythmogenicity of cardiac substrates. We modify the model to yield well-defined behavior for common experimental protocols and construct a spatially extended version to study emergent tissue dynamics. We find a complex action potential duration (APD) restitution behavior characterized by a non-monotonic dependence on pacing frequency. Electrotonic coupling in tissue leads not only to changes in action potential morphology but can also induce spatially concordant and discordant alternans not observed in the single-cell model. In two-dimensional tissue, our results show that the model supports stable functional reentry, whose frequency is in good agreement with that observed in adult mice. Our results can be used to further constrain and validate the mathematical model of neonatal mouse cardiomyocytes with future experiments

Phase-resolved analysis of the susceptibility of pinned spiral waves to far-field pacing in a two-dimensional model of excitable media

Life-threatening cardiac arrhythmias are associated with the existence of stable and unstable spiral waves. Termination of such complex spatio-temporal patterns by local control is substantially limited by anchoring of spiral waves at natural heterogeneities. Far-field pacing (FFP) is a new local control strategy that has been shown to be capable of unpinning waves from obstacles. In this article, we investigate in detail the FFP unpinning mechanism for a single rotating wave pinned to a heterogeneity. We identify qualitatively different phase regimes of the rotating wave showing that the concept of vulnerability is important but not sufficient to explain the failure of unpinning in all cases. Specifically, we find that a reduced excitation threshold can lead to the failure of unpinning, even inside the vulnerable window. The critical value of the excitation threshold (below which no unpinning is possible) decreases for higher electric field strengths and larger obstacles. In contrast, for a high excitation threshold, the success of unpinning is determined solely by vulnerability, allowing for a convenient estimation of the unpinning success rate. In some cases, we also observe phase resetting in discontinuous phase intervals of the spiral wave. This effect is important for the application of multiple stimuli in experiments

Multigenerational silencing dynamics control cell aging

Cellular aging plays an important role in many diseases, such as cancers, metabolic syndromes, and neurodegenerative disorders. There has been steady progress in identifying aging-related factors such as reactive oxygen species and genomic instability, yet an emerging challenge is to reconcile the contributions of these factors with the fact that genetically identical cells can age at significantly different rates. Such complexity requires single-cell analyses designed to unravel the interplay of aging dynamics and cell-to-cell variability. Here we use microfluidic technologies to track the replicative aging of single yeast cells and reveal that the temporal patterns of heterochromatin silencing loss regulate cellular life span. We found that cells show sporadic waves of silencing loss in the heterochromatic ribosomal DNA during the early phases of aging, followed by sustained loss of silencing preceding cell death. Isogenic cells have different lengths of the early intermittent silencing phase that largely determine their final life spans. Combining computational modeling and experimental approaches, we found that the intermittent silencing dynamics is important for longevity and is dependent on the conserved Sir2 deacetylase, whereas either sustained silencing or sustained loss of silencing shortens life span. These findings reveal that the temporal patterns of a key molecular process can directly influence cellular aging, and thus could provide guidance for the design of temporally controlled strategies to extend life span

Grid-Based Spectral Fiber Clustering

We introduce novel data structures and algorithms for clustering white matter fiber tracts to improve accuracy and robustness of existing techniques. Our novel fiber grid combined with a new randomized soft-division algorithm allows for defining the fiber similarity more precisely and efficiently than a feature space. A fine-tuning of several parameters to a particular fiber set- as it is often required if using a feature space- becomes obsolete. The idea is to utilize a 3D grid where each fiber point is assigned to cells with a certain weight. From this grid, an affinity matrix representing the fiber similarity can be calculated very efficiently in time O(n) in the average case, where n denotes the number of fibers. This is superior to feature space methods which need O(n 2) time. Our novel eigenvalue regression is capable of determining a reasonable number of clusters as it accounts for inter-cluster connectivity. It performs a linear regression of the eigenvalues of the affinity matrix to find the point of maximum curvature in a list of descending order. This allows for identifying inner clusters within coarse structures, which automatically and drastically reduces the a-priori knowledge required for achieving plausible clustering results. Our extended multiple eigenvector clustering exhibits a drastically improved robustness compared to the wellknown elongated clustering, which also includes an automatic detection of the number of clusters. We present several examples of artificial and real fiber sets clustered by our approach to support the clinical suitability and robustness of the proposed techniques