Guaranteed computation methods for compartmental in-series models under uncertainty

The pattern of some real phenomenon can be described by compartmental in-series models. Nevertheless, most of these processes are characterized by their variability, which produces that the exact values of the model parameters are uncertain, although they can be bounded by intervals. The aim of this paper is to compute tight solution envelopes that guarantee the inclusion of all possible behaviors of such processes. Current methods, such as monotonicity analysis, enable us to obtain guaranteed solution envelopes. However, if the model includes nonmonotone compartments or parameters, the computation of solution envelopes may produce a significant overestimation. Our proposal consists of performing a change of variables in which the output is unaltered, and the model obtained is monotone with respect to the uncertain parameters. The monotonicity of the new system allows us to compute the output bounds for the original system without overestimation. These model transformations have been developed for linear and non-linear systems. Furthermore, if the conditions are not completely satisfied, a novel method to compute tight solution envelopes is proposed. The methods exposed in this paper have been applied to compute tight solution envelopes for two different models: a linear system for glucose modeling and a non-linear system for an epidemiological model.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion through Grant DPI-2010-20764-C02-01, and by the Generalitat Valenciana through Grant GV/2012/085.De Pereda Sebastián, D.; Romero Vivó, S.; Ricarte Benedito, B.; Bondía Company, J. (2013). Guaranteed computation methods for compartmental in-series models under uncertainty. Computers and Mathematics with Applications. 66(9):1595-1605. https://doi.org/10.1016/j.camwa.2013.03.008S1595160566

On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach

Insulin therapy in type 1 diabetes aims to mimic the pattern of endogenous insulin secretion found in healthy subjects. Glucose-insulin models are widely used in the development of new predictive control strategies in order to maintain the plasma glucose concentration within a narrow range, avoiding the risks of high or low levels of glucose in the blood. However, due to the high variability of this biological process, the exact values of the model parameters are unknown, but they can be bounded by intervals. In this work, the computation of tight glucose concentration bounds under parametric uncertainty for the development of robust prediction tools is addressed. A monotonicity analysis of the model states and parameters is performed. An analysis of critical points, state transformations and application of differential inequalities are proposed to deal with non-monotone parameters. In contrast to current methods, the guaranteed simulations for the glucose-insulin model are carried out by considering uncertainty in all the parameters and initial conditions. Furthermore, no time-discretisation is required, which helps to reduce the computational time significantly. As a result, we are able to compute a tight glucose envelope that bounds all the possible patient's glycemic responses with low computational effort. (C) 2012 Elsevier Ireland Ltd. All rights reserved.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion through Grant DPI-2010-20764-C02, by the Universitat Politecnica de Valencia through Grant PAID-05-09-4334, and by the Generalitat Valenciana through Grant GV/2012/085.De Pereda Sebastián, D.; Romero Vivó, S.; Ricarte Benedito, B.; Bondía Company, J. (2012). On the prediction of glucose concentration under intra-patient variability in type 1 diabetes: A monotone systems approach. Computer Methods and Programs in Biomedicine. 108(3):993-1001. https://doi.org/10.1016/j.cmpb.2012.05.012S9931001108

On the computation of output bounds on parallel inputs pharmacokinetic models with parametric uncertainty

Pharmacokinetic models are of utmost importance in drug and medical research. The class of parallel inputs models consists of two or more linear chains connected together in parallel. It has been used to represent pharmacokinetic processes in which the input shows effects on the output with different delays in time. Due to physiological variability, the exact values of the model parameters are uncertain, but they can be bounded by intervals. In this case, the computation of output bounds can be posed as the solution of an initial value problem (IVP) for ordinary differential equations (ODEs) with uncertain initial conditions. However, current methods may produce a significant overestimation. In this paper, a new method to minimise overestimation when using the parallel inputs model is proposed and applied to two cases: subcutaneous insulin absorption for artificial pancreas research, and the study of the double-peak phenomenon observed for certain drugs. Our proposal consists in performing a model reduction in conjunction with analytical solutions of the input chains and a monotonicity analysis of model states and parameters. This method allows obtaining tighter output bounds with low computational cost compared to the latest techniques.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion through Grant DPI-2010-20764-C02, and by the Universitat Politecnica de Valencia through Grant PAID-05-09-4334.De Pereda Sebastián, D.; Romero Vivó, S.; Bondía Company, J. (2013). On the computation of output bounds on parallel inputs pharmacokinetic models with parametric uncertainty. Mathematical and Computer Modelling. 57:1760-1767. https://doi.org/10.1016/j.mcm.2011.11.031S176017675

Aplicación en el aula de una práctica informática para la Ingeniería Civil empleando el asistente Mathematica

In this paper, a computer laboratory for the subject Mathematical Methods for Civil Engineering is presented. These studies belong to the first year of every degree at Superior Technical School of Civil Engineers at Polytechnic University of Valencia. The laboratory chosen deals with the algebraic notions concerning Quadratic Forms, conics and Quadrics. Its development as well as its subsequent application in the lecture room from both a methodological and educational point of view is introduced. Moreover, the assessment carried out is analyzed. Finally, the results obtained by the students are separately shown depending on the degree they are enrolled in.En este trabajo se presenta una práctica de Informática de la asignatura Métodos Matemáticos para la Ingeniería Civil englobada dentro de las titulaciones referidas a los estudios de Ingeniería Civil que se imparten en la Universidad Politécnica de Valencia. La práctica elegida versa sobre los conceptos algebraicos relativos a Formas Cuadráticas, Cónicas y Cuádricas. Su desarrollo y posterior aplicación en el aula, tanto a nivel metodológico como didáctico, es introducido. Además, se analiza la evaluación llevada a cabo y se muestran los resultados obtenidos en función del tipo de titulación que esté cursando cada alumno