SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness

We deduce cell population models describing the evolution of a tumor (possibly interacting with its environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations of cancer cells allow accounting for the tumor heterogeneity. In our settings these include cancer stem cells known to be less sensitive to treatment and differentiated cancer cells having a higher sensitivity towards chemo- and radiotherapy. Our approach relies on stochastic differential equations in order to account for randomness in the system, arising e.g., due to the therapy-induced decreasing number of clonogens, which renders a pure deterministic model arguable. The equations are deduced relying on transition probabilities characterizing innovations of the two cancer cell subpopulations, and similarly extended to also account for the evolution of normal tissue. Several therapy approaches are introduced and compared by way of tumor control probability (TCP) and uncomplicated tumor control probability (UTCP). A PDE approach allows to assess the evolution of tumor and normal tissue with respect to time and to cell population densities which can vary continuously in a given set of states. Analytical approximations of solutions to the obtained PDE system are provided as well.RTI2018- 093416-B-I0

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

Competitive exclusion in a two-especies chemotasis model

We consider a mathematical model for the spatio-temporal evolution of two biological species in a competitive situation. Besides diffusing, both species move toward higher concentrations of a chemical substance which is produced by themselves. The resulting system consists of two parabolic equations with Lotka–Volterra-type kinetic terms and chemotactic cross-diffusion, along with an elliptic equation describing the behavior of the chemical. We study the question in how far the phenomenon of competitive exclusion occurs in such a context. We identify parameter regimes for which indeed one of the species dies out asymptotically, whereas the other reaches its carrying capacity in the large time limit

Parameter identification problems in the modelling of cell motility

We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree

Future Fitness of Female Insect Pests in Temporally Stable and Unstable Habitats and Its Impact on Habitat Utility as Refuges for Insect Resistance Management

The long-term fitness of individuals is examined in complex and temporally dynamic ecosystems. We call this multigeneration fitness measure “future fitness”. Helicoverpa zea (Boddie) (Lepidoptera: Noctuidae) is a polyphagous insect that feeds on many wild and cultivated hosts. While four generations of H. zea occur during the cropping season in the U.S. Mid Southern agroecosysem, the latter two generations were of most interest, as corn (which has been largely nontransgenic in the Mid-South) dominates the first two generations in the cropping system. In simulations of the evolution of resistance to Bt-transgenic crops, cotton refuge areas were found to be significantly more effective than similar soybean acreages at delaying the evolution of resistance. Cotton is a suitable host for H. zea during two late summer generations, while a soybean field is suitable for only one of these generations, therefore soybean fields of other maturity groups were simulated as being attractive during the alternative generation. A hypothetical soybean variety was tested in which a single field would be attractive over both generations and it was found to be significantly more effective at delaying resistance than simulated conventional soybean varieties. Finally, the placement of individuals emerging at the start of the 3rd (first without corn) generation was simulated in either refuge cotton, conventional soybean and the hypothetical long attractive soybean and the mean number of offspring produced was measured at the end of the season. Although females in conventional and long soybean crops had the same expected fecundity, because of differences in temporal stability of the two crops, the long soybean simulations had significantly more H. zea individuals at the end of the season than the conventional soybean simulations. These simulations demonstrate that the long-term fecundity associated with an individual is dependent not only on the fecundity of that individual in its current habitat, but also the temporal stability of habitats, the ecosystem at large and the likelihood that the individual's offspring will move into different habitats

Technology as 'Applied Science': a Serious Misconception that Reinforces Distorted and Impoverished Views of Science

The current consideration of technology as 'applied science', this is to say, as something that comes 'after' science, justifies the lack of attention paid to technology in science education. In our paper we question this simplistic view of the science-technology relationship, historically rooted in the unequal appreciation of intellectual and manual work, and we try to show how the absence of the technological dimension in science education contributes to a na¿ ve and distorted view of science which deeply affects the necessary scientific and technological literacy of all citizens

Malignant neuroendocrine tumour of the appendix in childhood with loco-regional lymph node invasion

The virtual slide(s) for this article can be found here: http://www.diagnosticpathology.diagnomx.eu/vs/1006600359152743 ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13000-015-0287-z) contains supplementary material, which is available to authorized users