Finite dimensional state representation of physiologically structured populations (vol 80, pg 205, 2020)

Correction to Journal of Mathematical Biology (2020) 80:205–273 https://doi.org/10.1007/s00285-019-01454-0In the original publication of the article, the Subsection 2.1.2 was published incorrectly.Peer reviewe

On models of physiologically structured populations and their reduction to ordinary differential equations

Considering the environmental condition as a given function of time, we formulate a physiologically structured population model as a linear non-autonomous integral equation for the, in general distributed, population level birth rate. We take this renewal equation as the starting point for addressing the following question: When does a physiologically structured population model allow reduction to an ODE without loss of relevant information? We formulate a precise condition for models in which the state of individuals changes deterministically, that is, according to an ODE. Specialising to a one-dimensional individual state, like size, we present various sufficient conditions in terms of individual growth-, death-, and reproduction rates, giving special attention to cell fission into two equal parts and to the catalogue derived in an other paper of ours (submitted). We also show how to derive an ODE system describing the asymptotic large time behaviour of the population when growth, death and reproduction all depend on the environmental condition through a common factor (so for a very strict form of physiological age).Peer reviewe

Finite dimensional state representation of physiologically structured populations

In a physiologically structured population model (PSPM) individuals are characterised by continuous variables, like age and size, collectively called their i-state. The world in which these individuals live is characterised by another set of variables, collectively called the environmental condition. The model consists of submodels for (i) the dynamics of the i-state, e.g. growth and maturation, (ii) survival, (iii) reproduction, with the relevant rates described as a function of (i-state, environmental condition), (iv) functions of (i-state, environmental condition), like biomass or feeding rate, that integrated over the i-state distribution together produce the output of the population model. When the environmental condition is treated as a given function of time (input), the population model becomes linear in the state. Density dependence and interaction with other populations is captured by feedback via a shared environment, i.e., by letting the environmental condition be influenced by the populations' outputs. This yields a systematic methodology for formulating community models by coupling nonlinear input-output relations defined by state-linear population models. For some combinations of submodels an (infinite dimensional) PSPM can without loss of relevant information be replaced by a finite dimensional ODE. We then call the model ODE-reducible. The present paper provides (a) a test for checking whether a PSPM is ODE reducible, and (b) a catalogue of all possible ODE-reducible models given certain restrictions, to wit: (i) the i-state dynamics is deterministic, (ii) the i-state space is one-dimensional, (iii) the birth rate can be written as a finite sum of environment-dependent distributions over the birth states weighted by environment independent 'population outputs'. So under these restrictions our conditions for ODE-reducibility are not only sufficient but in fact necessary. Restriction (iii) has the desirable effect that it guarantees that the population trajectories are after a while fully determined by the solution of the ODE so that the latter gives a complete picture of the dynamics of the population and not just of its outputs.Peer reviewe

The evolution of dispersal under demographic stochasticity.

abstract: Temporal and spatial variations of the environment are important factors favoring the evolution of dispersal. With few exceptions, these variations have been considered to be exclusively fluctuations of habitat quality. However, since the presence of conspecifics forms part of an individual's environment, demographic stochasticity may be a component of this variability as well, in particular when local populations are small. To study this effect, we analyzed the evolution of juvenile dispersal in a metapopulation model in which habitat quality is constant in space and time but occupancy fluctuates because of demographic stochasticity. Our analysis extends previous studies in that it includes competition of resources and competition for space. Also, juvenile dispersal is not given by a fixed probability but is made conditional on the presence of free territories in a patch, whereas individuals born in full patches will always disperse. Using a combination of analytical and numerical approaches, we show that demographic stochasticity in itself may provide enough variability to favor dispersal even from patches that are not fully occupied. However, there is no simple relationship between the evolution of dispersal and various indicators of demographic stochasticity. Selected dispersal depends on all aspects of the life-history profile, including kin selection

Evolution of Reproduction Periods in Seasonal Environments

Many species are subject to seasonal cycles in resource availability, affecting the timing of their reproduction. Using a stage-structured consumer-resource model in which juvenile development and maturation are resource dependent, we study how a species' reproductive schedule evolves, dependent on the seasonality of its resource. We find three qualitatively different reproduction modes. First, continuous income breeding (with adults reproducing throughout the year) evolves in the absence of significant seasonality. Second, seasonal income breeding (with adults reproducing unless they are starving) evolves when resource availability is sufficiently seasonal and juveniles are more efficient resource foragers. Third, seasonal capital breeding (with adults reproducing partly through the use of energy reserves) evolves when resource availability is sufficiently seasonal and adults are more efficient resource foragers. Such capital breeders start reproduction already while their offspring are still experiencing starvation. Changes in seasonality lead to continuous transitions between continuous and seasonal income breeding, but the change between income and capital breeding involves a hysteresis pattern, such that a population's evolutionarily stable reproduction pattern depends on its initial one. Taken together, our findings show how adaptation to seasonal environments can result in a rich array of outcomes, exhibiting seasonal or continuous reproduction with or without energy reserves

Cyto-mechanoresponsive polyelectrolyte multilayer films.

Cell adhesion processes take place through mechanotransduction mechanisms where stretching of proteins results in biological responses. In this work, we present the first cyto-mechanoresponsive surface that mimics such behavior by becoming cell-adhesive through exhibition of arginine-glycine-aspartic acid (RGD) adhesion peptides under stretching. This mechanoresponsive surface is based on polyelectrolyte multilayer films built on a silicone sheet and where RGD-grafted polyelectrolytes are embedded under antifouling phosphorylcholine-grafted polyelectrolytes. The stretching of this film induces an increase in fibroblast cell viability and adhesion.journal articleresearch support, non-u.s. gov't2012 Jan 112011 12 20importe

Automatic centerline extraction of coronary arteries in coronary computed tomographic angiography

Coronary computed tomographic angiography (CCTA) is a non-invasive imaging modality for the visualization of the heart and coronary arteries. To fully exploit the potential of the CCTA datasets and apply it in clinical practice, an automated coronary artery extraction approach is needed. The purpose of this paper is to present and validate a fully automatic centerline extraction algorithm for coronary arteries in CCTA images. The algorithm is based on an improved version of Frangi’s vesselness filter which removes unwanted step-edge responses at the boundaries of the cardiac chambers. Building upon this new vesselness filter, the coronary artery extraction pipeline extracts the centerlines of main branches as well as side-branches automatically. This algorithm was first evaluated with a standardized evaluation framework named Rotterdam Coronary Artery Algorithm Evaluation Framework used in the MICCAI Coronary Artery Tracking challenge 2008 (CAT08). It includes 128 reference centerlines which were manually delineated. The average overlap and accuracy measures of our method were 93.7% and 0.30 mm, respectively, which ranked at the 1st and 3rd place compared to five other automatic methods presented in the CAT08. Secondly, in 50 clinical datasets, a total of 100 reference centerlines were generated from lumen contours in the transversal planes which were manually corrected by an expert from the cardiology department. In this evaluation, the average overlap and accuracy were 96.1% and 0.33 mm, respectively. The entire processing time for one dataset is less than 2 min on a standard desktop computer. In conclusion, our newly developed automatic approach can extract coronary arteries in CCTA images with excellent performances in extraction ability and accuracy

Invasion and Persistence of Infectious Agents in Fragmented Host Populations

One of the important questions in understanding infectious diseases and their prevention and control is how infectious agents can invade and become endemic in a host population. A ubiquitous feature of natural populations is that they are spatially fragmented, resulting in relatively homogeneous local populations inhabiting patches connected by the migration of hosts. Such fragmented population structures are studied extensively with metapopulation models. Being able to define and calculate an indicator for the success of invasion and persistence of an infectious agent is essential for obtaining general qualitative insights into infection dynamics, for the comparison of prevention and control scenarios, and for quantitative insights into specific systems. For homogeneous populations, the basic reproduction ratio plays this role. For metapopulations, defining such an ‘invasion indicator’ is not straightforward. Some indicators have been defined for specific situations, e.g., the household reproduction number . However, these existing indicators often fail to account for host demography and especially host migration. Here we show how to calculate a more broadly applicable indicator for the invasion and persistence of infectious agents in a host metapopulation of equally connected patches, for a wide range of possible epidemiological models. A strong feature of our method is that it explicitly accounts for host demography and host migration. Using a simple compartmental system as an example, we illustrate how can be calculated and expressed in terms of the key determinants of epidemiological dynamics

Cardiovascular imaging 2011 in the International Journal of Cardiovascular Imaging

Cardiovascular Aspects of Radiolog