Testing and recommending methods for fitting size spectra to data

The size spectrum of an ecological community characterizes how a property, such as abundance or biomass, varies with body size. Size spectra are often used as ecosystem indicators of marine systems. They have been fitted to data from various sources, including groundfish trawl surveys, visual surveys of fish in kelp forests and coral reefs, sediment samples of benthic invertebrates and satellite remote sensing of chlorophyll.Over the past decades, several methods have been used to fit size spectra to data. We document eight such methods, demonstrating their commonalities and differences. Seven methods use linear regression (of which six require binning of data), while the eighth uses maximum likelihood estimation. We test the accuracy of the methods on simulated data.We demonstrate that estimated size-spectrum slopes are not always comparable between the seven regression-based methods because such methods are not estimating the same parameter. We find that four of the eight tested methods can sometimes give reasonably accurate estimates of the exponent of the individual size distribution (which is related to the slope of the size spectrum). However, sensitivity analyses find that maximum likelihood estimation is the only method that is consistently accurate, and the only one that yields reliable confidence intervals for the exponent.We therefore recommend the use of maximum likelihood estimation when fitting size spectra. To facilitate this, we provide documented R code for fitting and plotting results. This should provide consistency in future studies and improve the quality of any resulting advice to ecosystem managers. In particular, the calculation of reliable confidence intervals will allow proper consideration of uncertainty when making management decisions

Assessing the ability of substrate mapping techniques to guide ventricular tachycardia ablation using computational modelling

BACKGROUND: Identification of targets for ablation of post-infarction ventricular tachycardias (VTs) remains challenging, often requiring arrhythmia induction to delineate the reentrant circuit. This carries a risk for the patient and may not be feasible. Substrate mapping has emerged as a safer strategy to uncover arrhythmogenic regions. However, VT recurrence remains common. GOAL: To use computer simulations to assess the ability of different substrate mapping approaches to identify VT exit sites. METHODS: A 3D computational model of the porcine post-infarction heart was constructed to simulate VT and paced rhythm. Electroanatomical maps were constructed based on endocardial electrogram features and the reentry vulnerability index (RVI - a metric combining activation (AT) and repolarization timings to identify tissue susceptibility to reentry). Since scar transmurality in our model was not homogeneous, parameters derived from all signals (including dense scar regions) were used in the analysis. Potential ablation targets obtained from each electroanatomical map during pacing were compared to the exit site detected during VT mapping. RESULTS: Simulation data showed that voltage cut-offs applied to bipolar electrograms could delineate the scar, but not the VT circuit. Electrogram fractionation had the highest correlation with scar transmurality. The RVI identified regions closest to VT exit site but was outperformed by AT gradients combined with voltage cut-offs. The performance of all metrics was affected by pacing location. CONCLUSIONS: Substrate mapping could provide information about the infarct, but the directional dependency on activation should be considered. Activation-repolarization metrics have utility in safely identifying VT targets, even with non-transmural scars

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling

In vitro tumour spheroid experiments have been used to study avascular tumour growth and drug design for the last 50 years. Unlike simpler two-dimensional cell cultures, tumour spheroids exhibit heterogeneity within the growing population of cells that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing population, giving rise to the notion of a four-dimensional (4D) tumour spheroid. In this work we develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data qualitatively and quantitatively compare very well with experimental data from a suite of 4D tumour spheroid experiments performed with a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is very difficult to measure these data in standard tumour spheroid experiments. Software required to implement the IBM is available on GitHub, https://github.com/ProfMJSimpson/4DFUCCI

Constructing a Stochastic Model of Bumblebee Flights from Experimental Data

PMCID: PMC3592844This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Skin parasite landscape determines host infectiousness in visceral leishmaniasis

Increasing evidence suggests that the infectiousness of patients for the sand fly vector of visceral leishmaniasis is linked to parasites found in the skin. Using a murine model that supports extensive skin infection with Leishmania donovani, spatial analyses at macro-(quantitative PCR) and micro-(confocal microscopy) scales indicate that parasite distribution is markedly skewed. Mathematical models accounting for this heterogeneity demonstrate that while a patchy distribution reduces the expected number of sand flies acquiring parasites, it increases the infection load for sand flies feeding on a patch, increasing their potential for onward transmission. Models representing patchiness at both macro- and micro-scales provide the best fit with experimental sand fly feeding data, pointing to the importance of the skin parasite landscape as a predictor of host infectiousness. Our analysis highlights the skin as a critical site to consider when assessing treatment efficacy, transmission competence and the impact of visceral leishmaniasis elimination campaigns.Parasitemia has been considered the main determinant of visceral leishmaniasis transmission. By combining imaging, qPCR and experimental xenodiagnoses with mathematical models, Doehl et al. argue that the patchy landscape of parasites in the skin is necessary to explain infectiousness

A flexible mathematical model platform for studying branching networks : experimentally validated using the model actinomycete, Streptomyces coelicolor

Branching networks are ubiquitous in nature and their growth often responds to environmental cues dynamically. Using the antibiotic-producing soil bacterium Streptomyces as a model we have developed a flexible mathematical model platform for the study of branched biological networks. Streptomyces form large aggregates in liquid culture that can impair industrial antibiotic fermentations. Understanding the features of these could aid improvement of such processes. The model requires relatively few experimental values for parameterisation, yet delivers realistic simulations of Streptomyces pellet and is able to predict features, such as the density of hyphae, the number of growing tips and the location of antibiotic production within a pellet in response to pellet size and external nutrient supply. The model is scalable and will find utility in a range of branched biological networks such as angiogenesis, plant root growth and fungal hyphal networks

Modulation of ATP/ADP Concentration at the Endothelial Cell Surface by Flow: Effect of Cell Topography

Determining how flow affects the concentration of the adenine nucleotides ATP and ADP at the vascular endothelial cell (EC) surface is essential for understanding flow-induced mobilization of intracellular calcium. Previously, mathematical models were formulated to describe the ATP/ADP concentration at the EC surface; however, all previous models assumed the endothelium to be flat. In the present study we investigate the effect of surface undulations on ATP/ADP concentration at the EC surface. The results demonstrate that under certain geometric and flow conditions, the ATP + ADP concentration at the EC surface is considerably lower for a wavy cell surface than for a flat surface. Because ECs in regions of disturbed arterial flow are expected to have larger undulations than cells in non-disturbed flow zones, our findings suggest that ECs in regions of flow disturbance would exhibit lower ATP + ADP concentrations at their surfaces, which may lead to impaired calcium signaling. If validated experimentally, the present results may contribute to our understanding of endothelial cell dysfunction observed in regions of disturbed flow

Flow-Dependent Mass Transfer May Trigger Endothelial Signaling Cascades

It is well known that fluid mechanical forces directly impact endothelial signaling pathways. But while this general observation is clear, less apparent are the underlying mechanisms that initiate these critical signaling processes. This is because fluid mechanical forces can offer a direct mechanical input to possible mechanotransducers as well as alter critical mass transport characteristics (i.e., concentration gradients) of a host of chemical stimuli present in the blood stream. However, it has recently been accepted that mechanotransduction (direct mechanical force input), and not mass transfer, is the fundamental mechanism for many hemodynamic force-modulated endothelial signaling pathways and their downstream gene products. This conclusion has been largely based, indirectly, on accepted criteria that correlate signaling behavior and shear rate and shear stress, relative to changes in viscosity. However, in this work, we investigate the negative control for these criteria. Here we computationally and experimentally subject mass-transfer limited systems, independent of mechanotransduction, to the purported criteria. The results showed that the negative control (mass-transfer limited system) produced the same trends that have been used to identify mechanotransduction-dominant systems. Thus, the widely used viscosity-related shear stress and shear rate criteria are insufficient in determining mechanotransduction-dominant systems. Thus, research should continue to consider the importance of mass transfer in triggering signaling cascades

Implementing glucose control in intensive care: a multicenter trial using statistical process control

Glucose control (GC) with insulin decreases morbidity and mortality of critically ill patients. In this study we investigated GC performance over time during implementation of GC strategies within three intensive care units (ICUs) and in routine clinical practice. All adult critically ill patients who stayed for >24 h between 1999 and 2007 were included. Effects of implementing local GC guidelines and guideline revisions on effectiveness/efficiency-related indicators, safety-related indicators, and protocol-related indicators were measured. Data of 17,111 patient admissions were evaluated, with 714,141 available blood glucose levels (BGL) measurements. Mean BGL, time to reach target, hyperglycemia index, sampling frequency, percentage of hyperglycemia events, and in-range measurements statistically changed after introducing GC in all ICUs. The introduction of simple rules on GC had the largest effect. Subsequent changes in the protocol had a smaller effect than the introduction of the protocol itself. As soon as the protocol was introduced, in all ICUs the percentage of hypoglycemia events increased. Various revisions were implemented to reduce hypoglycemia events, but levels never returned to those from pre-implementation. More intensive implementation strategies including the use of a decision support system resulted in better control of the process. There are various strategies to achieve GC in routine clinical practice but with variable success. All of them were associated with an increase in hypoglycemia events, but GC was never stopped. Instead, these events have been accepted and managed. Statistical process control is a useful tool for monitoring phenomena over time and captures within-institution change