The use of mathematical and computational models for reliable predictions of tumor growth and decline in living organisms is one of the foremost challenges in modern predictive science, as it must cope with uncertainties in observational data, model selection, model parameters, and model inadequacy, all for very complex physical and biological systems. In this paper, large classes of parametric models of tumor growth in vascular tissue are discussed including models for radiation therapy. Observational data is obtained from MRI of a murine model of glioma and observed over a period of about three weeks, with X-ray radiation administered 14.5 days into the experimental program. Parametric models of tumor proliferation and decline are presented based on the balance laws of continuum mixture theory, particularly mass balance, and from accepted biological hypotheses on tumor growth. Among these are new model classes that include characterizations of effects of radiation and simple models of mechanical deformation of tumors. The Occam Plausibility Algorithm (OPAL) is implemented to provide a Bayesian statistical calibration of the model classes, 39 models in all, as well as the determination of the most plausible models in these classes relative to the observational data, and to assess model inadequacy through statistical validation processes. Discussions of the numerical analysis of finite element approximations of the system of stochastic, nonlinear partial differential equations characterizing the model classes, as well as the sampling algorithms for Monte Carlo and Markov chain Monte Carlo (MCMC) methods employed in solving the forward stochastic problem, and in computing posterior distributions of parameters and model plausibilities are provided. The results of the analyses described suggest that the general framework developed can provide a useful approach for predicting tumor growth and the effects of radiation.

A central question to biology is how pathogenic bacteria initiate acute or chronic infections. Here we describe a genetic program for cell-fate decision in the opportunistic human pathogen Staphylococcus aureus, which generates the phenotypic bifurcation of the cells into two genetically identical but different cell types during the course of an infection. Whereas one cell type promotes the formation of biofilms that contribute to chronic infections, the second type is planktonic and produces the toxins that contribute to acute bacteremia. We identified a bimodal switch in the agr quorum sensing system that antagonistically regulates the differentiation of these two physiologically distinct cell types. We found that extracellular signals affect the behavior of the agr bimodal switch and modify the size of the specialized subpopulations in specific colonization niches. For instance, magnesium-enriched colonization niches causes magnesium binding to S. aureusteichoic acids and increases bacterial cell wall rigidity. This signal triggers a genetic program that ultimately downregulates the agr bimodal switch. Colonization niches with different magnesium concentrations influence the bimodal system activity, which defines a distinct ratio between these subpopulations; this in turn leads to distinct infection outcomes in vitro and in an in vivo murine infection model. Cell differentiation generates physiological heterogeneity in clonal bacterial infections and helps to determine the distinct infection types.

We present a systematic study on higher-order penalty techniques for isogeometric mortar methods. In addition to the weak-continuity enforced by a mortar method, normal derivatives across the interface are penalized. The considered applications are fourth order problems as well as eigenvalue problems for second and fourth order equations. The hybrid coupling enables the discretization of fourth order problems in a multi-patch setting as well as a convenient implementation of natural boundary conditions. For second order eigenvalue problems, the pollution of the discrete spectrum -typically referred to as "outliers" -can be avoided.Numerical results illustrate the good behaviour of the proposed method in simple systematic studies as well as more complex multi-patch mapped geometries for linear elasticity and Kirchhoff plates.

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We show that optimal L 2 -convergence in the finite element method on quasi-uniform meshes can be achieved if, for some s 0 > 1/2, the boundary value problem has the mapping property H −1+s → H 1+s for s ∈ [0, s 0 ]. The lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained.