Mathematical Modeling of the Gastrointestinal System for Preliminary Drug Absorption Assessment.

The objective of this study is to demonstrate the potential of a multicompartmental mathematical model to simulate the activity of the gastrointestinal system after the intake of drugs, with a limited number of parameters. The gastrointestinal system is divided into five compartments, modeled as both continuous systems with discrete events (stomach and duodenum) and systems with delay (jejunum, ileum, and colon). The dissolution of the drug tablet occurs in the stomach and is described through the Noyes-Whitney equation, with pH dependence expressed through the Henderson-Hasselbach relationship. The boluses resulting from duodenal activity enter the jejunum, ileum, and colon compartments, where drug absorption takes place as blood flows countercurrent. The model includes only three parameters with assigned physiological meanings. It was tested and validated using data from in vivo experiments. Specifically, the model was tested with the concentration profiles of nine different drugs and validated using data from two drugs with varying initial concentrations. Overall, the outputs of the model are in good agreement with experimental data, particularly with regard to the time of peak concentration. The primary sources of discrepancy were identified in the concentration decay. The model's main strength is its relatively low computational cost, making it a potentially excellent tool for in silico assessment and prediction of drug adsorption in the intestine.

In-Silico Prediction of Oral Drug Bioavailability: A multi-boluses approach.

This work focuses on a new mathematical model able to describe in a simple manner the intestinal physiology, in order to better study drug absorption and bioavailability. The aim of our model is to overcome the limitations of physiological pharmacokinetics models of the literature, introducing a different modelling approach. The core of the new proposed model is a Discrete-Continuous Approach (DCA): a sequence of boluses travels in the investigated portion of the intestine, in counter-current with blood that flows in continuous mode. No empirical equations are implemented in this model. Simulation results show an excellent correlation between the predicted and experimental concentration profile used to validate our model. Our new approach provides a simple tool, with a good reliability, to analyze a very complex phenomenon, using only few parameters.

Closed-loop control of tumor growth by means of anti-angiogenic administration.

A tumor growth model accounting for angiogenic stimulation and inhibition is here considered, and a closed-loop control law is presented with the aim of tumor volume reduction by means of anti-angiogenic administration. To this end the output-feedback linearization theory is exploited, with the feedback designed on the basis of a state observer for nonlinear systems. Measurements are supposed to be acquired at discrete sampling times, and a novel theoretical development in the area of time-delay systems is applied in order to derive a continuous-time observer in spite of the presence of sampled measurements. The overall control scheme allows to set independently the control and the observer parameters thanks to the structural properties of the tumor growth model. Simulations are carried out in order to mimic a real experimental framework on mice. These results seem extremely promising: they provide very good performances according to the measurements sampling interval suggested by the experimental literature, and show a noticeable level of robustness against the observer initial estimate, as well as against the uncertainties affecting the model parameters.

Stochastic modeling of expression kinetics identifies messenger half-lives and reveals sequential waves of co-ordinated transcription and decay.

The transcriptome in a cell is finely regulated by a large number of molecular mechanisms able to control the balance between mRNA production and degradation. Recent experimental findings have evidenced that fine and specific regulation of degradation is needed for proper orchestration of a global cell response to environmental conditions. We developed a computational technique based on stochastic modeling, to infer condition-specific individual mRNA half-lives directly from gene expression time-courses. Predictions from our method were validated by experimentally measured mRNA decay rates during the intraerythrocytic developmental cycle of Plasmodium falciparum. We then applied our methodology to publicly available data on the reproductive and metabolic cycle of budding yeast. Strikingly, our analysis revealed, in all cases, the presence of periodic changes in decay rates of sequentially induced genes and co-ordination strategies between transcription and degradation, thus suggesting a general principle for the proper coordination of transcription and degradation machinery in response to internal and/or external stimuli.

Observer-based techniques for the identification and analysis of avascular tumor growth.

Cancer represents one of the most challenging issues for the biomedical research, due its large impact on the public health state. For this reason, many mathematical methods have been proposed to forecast the time evolution of cancer size and invasion. In this paper, we study how to apply the Gompertz's model to describe the growth of an avascular tumor in a realistic setting. To this aim, we introduce mathematical techniques to discretize the model, an important requirement when discrete-time measurements are available. Additionally, we describe observed-based techniques, borrowed from the field of automation theory, as a tool to estimate the model unknown parameters. This identification approach is a promising alternative to traditional statistical methods, and it can be easily extended to other models of cancer growth as well as to the evaluation of not measurable variables, on the basis of the available measurements. We show an application of this method to the analysis of solid tumor growth and parameters estimation in presence of a chemotherapy agent.