Marie-Anne Lefebvre

Safety verification and reachability analysis for hybrid systems

Safety verification and reachability analysis for hybrid systems is a very active research domain. Many approaches that seem quite different, have been proposed to solve this complex problem. This paper presents an overview of various approaches for autonomous, continuous-time hybrid systems and presents them with respect to basic problems related to verification.

Modelling the influence of activation-induced apoptosis of CD4 + and CD8 + T-cells on the immune system response of a HIV-infected patient

On the basis of the human immunodeficiency virus (HIV) infection dynamics model proposed by Adams, the authors propose an extended model that aims at incorporating the influence of activation-induced apoptosis of CD4+ and CD8+ T-cells on the immune system response of HIV-infected patients. Through this model, the authors study the influence of this phenomenon on the time evolution of specific cell populations such as plasma concentrations of HIV copies, or blood concentrations of CD4+ and CD8+ T-cells. In particular, this study shows that depending on its intensity, the apoptosis phenomenon can either favour or mitigate the long-term evolution of the HIV infection.

A Closed-Loop Artificial Pancreas Using a Proportional Integral Derivative with Double Phase Lead Controller Based on a New Nonlinear Model of Glucose Metabolism

Background: Most closed-loop insulin delivery systems rely on model-based controllers to control the blood glucose (BG) level. Simple models of glucose metabolism, which allow easy design of the control law, are limited in their parametric identification from raw data. New control models and controllers issued from them are needed. Methods: A proportional integral derivative with double phase lead controller was proposed. Its design was based on a linearization of a new nonlinear control model of the glucose-insulin system in type 1 diabetes mellitus (T1DM) patients validated with the University of Virginia/Padova T1DM metabolic simulator. A 36 h scenario, including six unannounced meals, was tested in nine virtual adults. A previous trial database has been used to compare the performance of our controller with their previous results. The scenario was repeated 25 times for each adult in order to take continuous glucose monitoring noise into account. The primary outcome was the time BG levels were in target (70–180 mg/dl). Results: Blood glucose values were in the target range for 77% of the time and below 50 mg/dl and above 250 mg/dl for 0.8% and 0.3% of the time, respectively. The low blood glucose index and high blood glucose index were 1.65 and 3.33, respectively. Conclusion: The linear controller presented, based on the linearization of a new easily identifiable nonlinear model, achieves good glucose control with low exposure to hypoglycemia and hyperglycemia.

HYBRID ABSTRACTIONS OF AFFINE SYSTEMS

Abstract This paper considers the problem of building a set of hybrid abstractions for affine systems in order to compute over approximations of the reachable space. Each abstraction is based on a partition of the continuous state space that is defined by hyperplanes generated by near combinations of two vectors. The choice of these vectors is based on considerations on the dynamics of the system and uses, for example, the left eigen vectors of the matrix that defines this dynamics. It is shown how the reachability calculus can then be performed on a composition of such abstractions and how its accuracy depends on the choice of hyperplanes that defines the abstraction but also on the number of abstractions that are composed.

STRUCTURED HYBRID ABSTRACTIONS OF CONTINUOUS SYSTEMS.

Abstract Abstracting a continuous dynamical system by a hybrid linear automaton allows to use formal verification techniques to check properties of hybrid systems. In order to build the abstract model, the state space is partitioned and the rate of each state variable is approximated. When the system is linear the properties of the continuous system can be used to split the state space in order to get a tighter abstraction with an automaton that remains simple, so that the reachability calculus is more accurate. Moreover the accuracy of the approximation can be used to aid the design of the partition.

A Mobile Application Guiding Patients With Type 1 Diabetes Using Sensor-Augmented Insulin Pump Therapy:

Real-time continuous glucose monitoring (RT-CGM) generates abundant data which patients may find challenging—current glucose level, direction and rate of change, retrospective data—all needing to be properly interpreted according to the different events of a single day (meals, snacks, physical activity, sleep). These findings led us to the development of a mobile application, Insulin Pump Real-Time Advisor (IPRA©), designed to translate RT-CGM technology into an efficient self-management tool for diabetic patients using sensor-augmented insulin pump (SAP) therapy, aiming to help them with safety and insulin adjustment decisions. The objective of this study was to assess the acceptance and reliability of this mobile application. The application algorithm takes into account current sensor glucose values and trends, on-going activities and time elapsed since previous meal. Six type 1 diabetic patients already using SAP therapy tested it for 2 weeks. Before advice was delivered, they had to specify their own spontaneous attitude (blinded evaluation). They then had to assess advice delivered and to suggest an alternative response if needed (unblinded evaluation) (Figure 1). Joint-probability agreement was used to assess agreement between the application and the patients’ response in blinded and unblinded conditions. Rates of unblinded agreement according to the situation (time since last meal and relation to bedtime, glucose level, glucose trends) were compared with the Fisher test. Satisfaction was assessed. A total of 238 situations was generated. Advice could combine various proposals, for example, “sugar intake or reduce basal rate to 50 or 70% of usual rate for 1 or 2 hours,” “check sensor glucose level in 30 minutes.” Rate of blinded agreement was 46% (125/270). Final unblinded agreement rate was 93% (250/270). Neither glucose level nor glucose trends had a significant impact. Unblinded agreement was lower for advice delivered at bedtime (82% vs 96% before a meal and 89% after a meal; P = .02). Mean satisfaction score was 4.2/5 (usefulness 4.7/5 ± 0.39, ergonomics 4.7/5 ± 0.29, impact 3.6/5 ± 0.95). The algorithm was approved by patients. Satisfaction was high, with a high final unblinded agreement rate contrasting with a rather low initial blinded agreement rate. Among the discrepancies, the patients’ judgment was considered right in 7 cases, mostly consisting in patients suggesting checking of blood glucose, and application advice will therefore be updated. On the other hand, in 43 other situations, the spontaneous decisions of patients were considered to be inadequate behaviors, which would have been ill-adapted or dangerous. Such inappropriate reactions have been reported in STAR 1 study, possibly attributable to a misuse of RT-CGM. These findings suggest that such an application could help to prevent inadequate behaviors and be used as a real-time educational tool. It might be especially useful at initiation of RT-CGM, as suggested by the results of Jenkins et al study. An upgraded version is being developed, including a bolus calculator taking insulin on-board into account, information on food carbohydrate content for glucose counting, and modulation of advice if exercise is planned. A prospective study at initiation of RT-CGM is needed to assess impact on metabolic parameters, behavior, and satisfaction. 633486 DSTXXX10.1177/1932296816633486Journal of Diabetes Science and TechnologyEsvant et al letter2016

A New Model for Closed-Loop Control in Type 1 Diabetes

A new control model for T1DM is designed with the aim to represent accurately the plasma glucose-insulin dynamics. It is in the form of a nonlinear system of three timecontinuous state equations. The model includes two successive remote compartments for plasma insulin, accounting for a slow and a fast dynamics. The modeling of the action of the insulin on the glucose disappearance is in an original nonlinear form. This new model is identified and validated using data from the adult subjects of the UVa T1DM simulator training database. The parametric identification of the model provides in each case an accurate representation of the glucose-insulin dynamics of the subjects.

Abstraction based reachability computation for affine systems with bounded input

Reachability computation is the central problem of verification of hybrid or continuous systems. One approach, among others, to compute an over approximation of the reachable space is to split the continuous state space and to abstract the continuous dynamics in each cell by a linear differential inclusion for which the reachable space may be computed with polyhedra. Previous works proposed to use characteristics of the affine continuous dynamics to guide the decomposition and this paper considers the extension of this approach to systems with bounded input. It is shown that considering the vertices of the boundary of the input domain, the decomposition is still useful to perform the reachability analysis. An algorithm is then proposed and exemplified

Manual Closed-Loop Insulin Delivery Using a Saddle Point Model Predictive Control Algorithm: Results of a Crossover Randomized Overnight Study:

Background: The purpose was to assess the efficacy of a new closed-loop algorithm (Saddle Point Model Predictive Control, SP-MPC) in achieving nocturnal normoglycemia while reducing the risk of hypoglycemia in patients with type 1 diabetes. Method: In this randomized crossover study, 10 adult patients (mean hemoglobin A1c 7.35 ± 1.04%) were assigned to be treated overnight by open loop using sensor-augmented pump therapy (open-loop SAP) or manual closed-loop delivery. During closed loop, insulin doses were calculated using the SP-MPC algorithm and administered as manual boluses every 15 minutes from 9:00 pm to 8:00 am. Patients consumed a self-selected meal (65-125 g of carbohydrates) at 7:00 pm accompanied by their usual prandial bolus. Blood glucose was measured every 30 minutes. The primary endpoints were the time spent in target (70-145 mg/dl) and time spent below 70 mg/dl from 11:00 pm to 8:00 am. Results: Time spent in target did not differ between closed-loop and open-loop SAP. The number of hypoglycemic events (<70 mg/dl) was reduced 2.8-fold in closed loop (n = 5, median = 0/patient/hour; interquartile range: 0-0.11) as compared to open-loop SAP (n = 14, median = 0.22/patient/hour, 0.02-0.22) (P = .02). The area under the curve for sensor glucose values >145 mg/dl was significantly lower during closed-loop than during open-loop SAP (P = .03) as well as HBGI (P = .02). Conclusions: This pilot study suggests that the use of the SP-MPC algorithm may improve mean overnight glucose control and reduce the number of hypoglycemic events as compared to SAP therapy.

Reachability analysis for nonlinear systems by guaranteed piecewise affine approximation

In this paper, we present an approach able to analysis reachability of non-linear hybrid systems. Using the hybridization method, it is possible to construct an approximation of the non-linear systems, in the form of piecewise affine systems with uncertainties, for which efficient approaches for computing reachability have been proposed. To do this, we first generate a partition of the state space of the nonlinear system. Then, we approximate locally, in each element of this partition, the non-linear system by an affine one. Finally, we add the approximation error in the affine model. In this way, instead of studying a complex non-linear systems we study locally an affine system with uncertainty.