Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.

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The apparent permeability index is widely used as part of a general screening process to study drug absorption, and is routinely obtained from in vitro or ex vivo experiments. A classical example, widely used in the pharmaceutical industry, is the in vitro Caco-2 cell culture model. The index is defined as the initial flux of compound through the membrane (normalized by membrane surface area and donor concentration) and is typically computed by adapting a straight line to the initial portion of the recorded amounts in the receiver compartment, possibly disregarding the first few points when lagging of the transfer process through the membrane is evident. Modeling the transfer process via a two-compartmental system yields an immediate analogue of the common Papp as the initial slope of the receiver quantity, but the two-compartment model often does not match observations well. A three-compartment model, describing the cellular layer as well as donor and receiver compartments, typically better represents the kinetics, but has the disadvantage of always having zero initial flow rate to the receiver compartment: in these circumstances the direct analogue of the Papp index is not informative since it is always zero. In the present work an alternative definition of an apparent permeability index is proposed for three-compartment models, and is shown to reduce to the classical formulation as the cellular layer's volume tends towards zero. This new index characterizes the intrinsic permeability of the membrane to the compound under investigation, can be directly computed in a completely observer-independent fashion, and reduces to the usual Papp when the linear two-compartment representation is sufficient to accurately describe compound kinetics.

With increasing pressure to accelerate drug development and minimize associated costs, it has become critical for pharmaceutical companies to optimize the clinical supply chain. Various tools have been developed to improve forecasts of medication requirements, some of them based on Monte Carlo simulation techniques. In this paper, we describe an innovative approach that goes beyond simulating trials with a priori supply strategies. This approach optimizes the supply plan by balancing the various costs against the risk of running out of medication and utilizes the Bayesian principle to reevaluate supply strategies over time. Supporting methodologies and processes, key to a successful implementation, are also emphasized.

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