Mechanisms of prion disease progression: a chemical reaction network approach.

Fatal neurodegenerative diseases such as bovine spongiform encephalopathy in cattle, scrapie in sheep and Creutzfeldt-Jakob disease in humans are caused by prions. Prion is a protein encoded by a normal cellular gene. The cellular form of the prion, namely PrP(C), is benign but can be converted into a disease-causing form (named scrapie), PrP(Sc), by a conformational change from -helix to -sheets. Prions replicate by this conformational change; that is, PrP(Sc) interacts with PrP(C) producing a new molecule of PrP(Sc). This kind of replication is modelled in this contribution as an autocatalytic process. The kinetic model accounts for two of the three epidemiological manifestations: sporadic and infectious. By assuming irreversibility of the PrP(Sc) replication and describing a first-order reaction for the degradation of cellular tissue, the authors explore dynamical scenarios for prion progression, such as oscillations and conditions for multiplicity of equilibria. Feinberg's chemical reaction network theory is exploited to identify multiple steady states and their associate kinetic constants.

Multiscroll attractors by switching systems.

In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable "one-spiral" trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.

Theoretical blood glucose control in hyper- and hypoglycemic and exercise scenarios by means of an H(infinity) algorithm.

Artificial Endocrine Pancreas (AEP) is one of the most optimistic approaches in Type 1 Diabetes Mellitus (T1DM) treatment due to the novel technological advances in continuous glucose monitoring, exogenous insulin delivery, and their proofs in clinical assessments. The main goal of AEP is to replace the pancreatic insulin secretion in the blood glucose regulation loop by means of an automatic exogenous insulin infusion. The joint element between glucose sensing and insulin delivering actions is an automatic algorithm-based decision. In this contribution, there is an H(infinity) control algorithm to compute the insulin infusion rate during hyperglycemia, exercise and nocturnal hypoglycemia. In order to mimic the insulin release pattern of a healthy pancreas, a frequency restriction in the insulin infusion pattern generated by controller was considered in the design. The inclusion of mathematical models of relations between glucose and chosen biosignals in the control loop generates an adequate insulin infusion pattern to compensate blood glucose variations during each metabolic scenario. The proposed automatic algorithm for decision shows good performance in controlling glycemia in metabolic scenarios, avoiding long-term hyperglycemia as well as glycemic disturbances during exercise and nocturnal hypoglycemia, guaranteeing insulin infusion with a delivery pattern closer to that generated by a healthy pancreas.

On hyperglicemic glucose basal levels in Type 1 Diabetes Mellitus from dynamic analysis.

Compartmental-Physiological Models (CPM's) have been used to derive feedback controllers for the glucose regulation in Diabetes Mellitus (DM). Despite these important advances, there are two criticisms about the use of the CPM's in DM: (i) Can this class of model reproduce severe basal glucose levels (e.g., larger than 300 mg/dl)? and (ii) Does a CPM reproduce a distinct glucose level as its parameters change or is it unique even if its parameters change? This contribution aims these criticisms from the study of the parametric sensitivity of a CPM. The results exploit the analysis of the dynamic properties of the chosen CPM and permit to show that such model can reproduce distinct severe basal levels by modifying the values of the metabolic parameters, which agree with expectations on a realistic model. Mainly, the chosen CPM has been selected due to the following two reasons. (i) It includes the main organs related to the glucose metabolism in Type 1 Diabetes Mellitus (T1DM); as, for example, the liver, brain and kidney. (ii) It models metabolic phenomena as, for instance, the counter-regulatory effects by glucagon and the hepatic glucose uptake/production. Additionally, the chosen model has been recently used to design feedback controllers for the glucose regulation with very promissory results.

Fuzzy-based controller for glucose regulation in type-1 diabetic patients by subcutaneous route.

This paper presents an advisory/control algorithm for a type-1 diabetes mellitus (TIDM) patient under an intensive insulin treatment based on a multiple daily injections regimen (MDIR). The advisory/control algorithm incorporates expert knowledge about the treatment of this disease by using Mamdani-type fuzzy logic controllers to regulate the blood glucose level (BGL). The overall control strategy is based on a two-loop feedback strategy to overcome the variability in the glucose-insulin dynamics from patient to patient. An inner-loop provides the amount of both rapid/short and intermediate/long acting insulin (RSAI and ILAI) formulations that are programmed in a three-shots daily basis before meals. The combined preparation is then injected by the patient through a subcutaneous route. Meanwhile, an outer-loop adjusts the maximum amounts of insulin provided to the patient in a time-scale of days. The outer-loop controller aims to work as a supervisor of the inner-loop controller. Extensive closed-loop simulations are illustrated, using a detailed compartmental model of the insulin-glucose dynamics in a TIDM patient with meal intake.

Complete synchronizability of chaotic systems: a geometric approach.

Synchronizability of chaotic systems is studied in this contribution. Geometrical tools are used to understand the properties of vector fields in affine systems. The discussion is focused on synchronizability of chaotic systems with equal order. The analysis is based on the synchronous behavior of all states of the master/slave system (complete synchronization). We state sufficient and necessary conditions for complete synchronizability which are based on controllability and observability of nonlinear affine systems. In this sense, the synchronizability is studied for complete synchronization via state feedback control.