A metamodel-based flexible insulin therapy for type 1 diabetes patients subjected to aerobic physical activity.

Patients with type 1 diabetes are subject to exogenous insulin injections, whether manually or through (semi)automated insulin pumps. Basic knowledge of the patient's characteristics and flexible insulin therapy (FIT) parameters are then needed. Specifically, artificial pancreas-like closed-loop insulin delivery systems are some of the most promising devices for substituting for endogenous insulin secretion in type 1 diabetes patients. However, these devices require self-reported information such as carbohydrates or physical activity from the patient, introducing potential miscalculations and delays that can have life-threatening consequences. Here, we display a metamodel for glucose-insulin dynamics that is subject to carbohydrate ingestion and aerobic physical activity. This metamodel incorporates major existing knowledge-based models. We derive comprehensive and universal definitions of the underlying FIT parameters to form an insulin sensitivity factor (ISF). In addition, the relevance of physical activity modelling is assessed, and the FIT is updated to take physical exercise into account. Specifically, we cope with physical activity by using heart rate sensors (watches) with a fully automated closed insulin loop, aiming to maximize the time spent in the glycaemic range (75.5% in the range and 1.3% below the range for hypoglycaemia on a virtual patient simulator).These mathematical parameter definitions are interesting on their own, may be new tools for assessing mathematical models and can ultimately be used in closed-loop artificial pancreas algorithms or to extend distinguished FIT.

Structure-based identification of sensor species for anticipating critical transitions.

Ecological systems can undergo sudden, catastrophic changes known as critical transitions. Anticipating these critical transitions remains challenging in systems with many species because the associated early warning signals can be weakly present or even absent in some species, depending on the system dynamics. Therefore, our limited knowledge of ecological dynamics may suggest that it is hard to identify those species in the system that display early warning signals. Here, we show that, in mutualistic ecological systems, it is possible to identify species that early anticipate critical transitions by knowing only the system structure-that is, the network topology of plant-animal interactions. Specifically, we leverage the mathematical theory of structural observability of dynamical systems to identify a minimum set of "sensor species," whose measurement guarantees that we can infer changes in the abundance of all other species. Importantly, such a minimum set of sensor species can be identified by using the system structure only. We analyzed the performance of such minimum sets of sensor species for detecting early warnings using a large dataset of empirical plant-pollinator and seed-dispersal networks. We found that species that are more likely to be sensors tend to anticipate earlier critical transitions than other species. Our results underscore how knowing the structure of multispecies systems can improve our ability to anticipate critical transitions.

From the hospital scale to nationwide: observability and identification of models for the COVID-19 epidemic waves.

Two mathematical models of the COVID-19 dynamics are considered as the health system in some country consists in a network of regional hospital centers. The first macroscopic model for the virus dynamics at the level of the general population of the country is derived from a standard SIR model. The second local model refers to a single node of the health system network, i.e. it models the flows of patients with a smaller granularity at the level of a regional hospital care center for COVID-19 infected patients. Daily (low cost) data are easily collected at this level, and are worked out for a fast evaluation of the local health status thanks to control systems methods. Precisely, the identifiability of the parameters of the hospital model is proven and thanks to the availability of clinical data, essential characteristics of the local health status are identified. Those parameters are meaningful not only to alert on some increase of the infection, but also to assess the efficiency of the therapy and health policy.

Hypoglycaemia-free artificial pancreas project.

Driving blood glycaemia from hyperglycaemia to euglycaemia as fast as possible while avoiding hypoglycaemia is a major problem for decades for type-1 diabetes and is solved in this study. A control algorithm is designed that guaranties hypoglycaemia avoidance for the first time both from the theory of positive systems point of view and from the most pragmatic clinical practice. The solution consists of a state feedback control law that computes the required hyperglycaemia correction bolus in real-time to safely steer glycaemia to the target. A rigorous proof is given that shows that the control-law respects the positivity of the control and of the glucose concentration error: as a result, no hypoglycaemic episode occurs. The so-called hypo-free strategy control is tested with all the UVA/Padova T1DM simulator patients (i.e. ten adults, ten adolescents, and ten children) during a fasting-night scenario and in a hybrid closed-loop scenario including three meals. The theoretical results are assessed by the simulations on a large cohort of virtual patients and encourage clinical trials.

A theoretical framework for controlling complex microbial communities.

Microbes form complex communities that perform critical roles for the integrity of their environment or the well-being of their hosts. Controlling these microbial communities can help us restore natural ecosystems and maintain healthy human microbiota. However, the lack of an efficient and systematic control framework has limited our ability to manipulate these microbial communities. Here we fill this gap by developing a control framework based on the new notion of structural accessibility. Our framework uses the ecological network of the community to identify minimum sets of its driver species, manipulation of which allows controlling the whole community. We numerically validate our control framework on large communities, and then we demonstrate its application for controlling the gut microbiota of gnotobiotic mice infected with Clostridium difficile and the core microbiota of the sea sponge Ircinia oros. Our results provide a systematic pipeline to efficiently drive complex microbial communities towards desired states.

Model Free iPID Control for Glycemia Regulation of Type-1 Diabetes.

OBJECTIVE: The objective is to design a fully automated glycemia controller of Type-1 Diabetes (T1D) in both fasting and postprandial phases on a large number of virtual patients. METHODS: A model-free intelligent proportional-integral-derivative (iPID) is used to infuse insulin. The feasibility of iPID is tested in silico on two simulators with and without measurement noise. The first simulator is derived from a long-term linear time-invariant model. The controller is also validated on the UVa/Padova metabolic simulator on 10 adults under 25 runs/subject for noise robustness test. RESULTS: It was shown that without measurement noise, iPID mimicked the normal pancreatic secretion with a relatively fast reaction to meals as compared to a standard PID. With the UVa/Padova simulator, the robustness against CGM noise was tested. A higher percentage of time in target was obtained with iPID as compared to standard PID with reduced time spent in hyperglycemia. CONCLUSION: Two different T1D simulators tests showed that iPID detects meals and reacts faster to meal perturbations as compared to a classic PID. The intelligent part turns the controller to be more aggressive immediately after meals without neglecting safety. Further research is suggested to improve the computation of the intelligent part of iPID for such systems under actuator constraints. Any improvement can impact the overall performance of the model-free controller. SIGNIFICANCE: The simple structure iPID is a step for PID-like controllers since it combines the classic PID nice properties with new adaptive features.

A Long-Term Model of the Glucose-Insulin Dynamics of Type 1 Diabetes.

A new glucose-insulin model is introduced which fits with the clinical data from in- and outpatients for two days. Its stability property is consistent with the glycemia behavior for type 1 diabetes. This is in contrast to traditional glucose-insulin models. Prior models fit with clinical data for a few hours only or display some nonnatural equilibria. The parameters of this new model are identifiable from standard clinical data as continuous glucose monitoring, insulin injection, and carbohydrate estimate. Moreover, it is shown that the parameters from the model allow the computation of the standard tools used in functional insulin therapy as the basal rate of insulin and the insulin sensitivity factor. This is a major outcome as they are required in therapeutic education of type 1 diabetic patients.

Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review.

This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.