Schedule for Workshop , Middelfart

s for talks on Workshop Wednesday, August 13 9:00 – 9:45 Kashayar Pakdaman, ISC PIF Paris 9:45 – 10:30 Carlos Braumann, Department of Mathematics and CIMA (Centro de Investigação em Matemática e Aplicações), Universidade de Évora, Portugal Stochastic differential equation models for population and individual growth and for harvesting in randomly varying environments The growth of a population living in a randomly varying environment (that affects birth and death rates) can be modelled by a stochastic differential equation (SDE) describing the dynamics of population size (number of individuals, biomass of a fishery,?). Stochastic differential equations can also be used to model the growth in size (weight, volume, length,?) from birth to maturity of individual animals or plants living in a randomly varying environment. Many SDE models have been proposed in the literature, some of them for both phenomena. It is worth saying that the traditional regression models are appropriate to model observational errors but totally inadequate to model these phenomena. In fact, they do not keep memory of past sizes and a population (or individual) with a size substantially below model average has an equal probability of having a size above or below model average in the immediate future. This is clearly a non realistic property. SDE models, on the contrary, always consider the present situation and project it into the future using the dynamics of the growth process (and also how it is affected by the random environmental fluctuations). Contrary to what is customary in the literature, instead of considered specific SDE models, we have obtained results on extinction and existence of a stationary density valid for a general class of SDE models (with mild assumptions mostly dictated by biological considerations). Such results are therefore model robust. Models for populations subjected to harvesting were considered as well. We have also studied the time to population extinction (for the population growth models) and the time to reach a maturity size (for the individual growth models). Here, we review those results. Examples of application to real data (for specific models) will be shown, including the issues of parameter estimation and prediction. 11:05 – 11:25 Cesar Palerm, Medtronic Diabetes and technology: Managing a complex disease People with type 1 diabetes must frequently adjust their insulin dosing in order to maintain glucose levels as close to normal as possible. This represents a daily challenge, as many different forces influence glycemia, such as diet and meal composition, exercise and its intensity level, hormonal fluctuations, as well as stress, be it physical or psychological. Technology has significantly improved the quality, and length, of life for those individuals with type 1 diabetes. Starting with the discovery and purification of insulin, on to home blood glucose meters, to designer insulins, subcutaneous infusion pumps, and more recently continuous glucose meters, each technology has had its impact. Nonetheless, these patients remain at increased risk for cardiovascular disease, increased morbidity and mortality when critically ill, and many other undesirable outcomes. This talk will give an overview of type 1 diabetes and the challenges patients face in managing their glucose levels. 11:25 – 12:00 Cesar Palerm, Medtronic Diabetes and technology: Towards an ”artificial pancrease” For people with type 1 diabetes the ultimate goal is complete normalization of blood glucose levels, as evidence suggests that even small deviations increase the risk of complications. While easy to say this is a formidable task, as patients need to frequently measure blood glucose levels, estimate meal carbohydrate content, and determine insulin dosing needs. Illness, exercise, stress and several other factors all affect glucose levels, making this a non-trivial problem. Because of this, the holy grail in diabetes management has been the development of an artificial pancreatic β-cell. This is a fully automated closed-loop system which will use the signal from a continuous glucose sensor to adjust insulin infusion rates in real-time. Although significant progress has been made, many hurdles remain. This talk will focus on the development of such a system at Medtronic Diabetes. Results from clinical trials will be presented, and an overview of the remaining challenges will be provided. 14:00 – 14:35 Robert Parker, University of Pittsburgh Modeling for Diabetes Control Beyond Insulin and Glucose Since the discovery of insulin by Banting and Best, the primary foci of Diabetes diagnosis and treatment have been glucose and insulin. While this does encompass the minimum necessary set, as continued brain function requires adequate glucose supply, other endogenous and exogenous compounds and disturbances are of increasing importance. More than 20 years ago, glucagon, which is released from the alpha-cells of the pancreas, was incorporated into mathematical models of diabetic patients due to the upregulatory effect of glucagon on hepatic glucose release. This talk presents a view of metabolism that looks beyond the glucose-insulin relationship to encompass additional key variables, particularly fatty acids and exercise. Fatty acids are the primary source of energy for the body, providing as much as 80% of the energy demand at rest. Interactions between fatty acids and glucose exist, as both are energy-providing substrates, and these interactions may impact both insulin demand and glucose control. In the case of a model-based control scheme, the choice to not account for fatty acid dynamics yields patient-model mismatch, which could impact the performance of a closed-loop device. Exercise is commonly prescribed for glucose management in diabetic patients; the dynamics and intensity of exercise characterize this substrate sink that impacts insulin, glucose, and fatty acids. We model the response of glucose-insulin interactions based on physiological response to mild-to-moderate exercise (below the anaerobic threshold). This provides a complimentary disturbance to meal consumption, the most common disturbance explored in the literature, by challenging the patient model with a decrease in circulating substrate levels. One approach to modeing is the so-called ”Minimal”approach of Cobelli and co-authors. Their 3-state mathematical model of glucose-insulin interactions, which includes a remote insulin action compartment, is perhaps the most well-studied diabetes model in the literature. Following their philosophy, we synthesized an extended minimal model that includes fatty acid dynamics. The result is a moderately-sized ODE-based model that includes mixed meal consumption. Alternatively, one can model based on the physiology of the system. Detailed models of glucose, insulin, and fatty acids were constructed based on mass balances around physiological tissues of interest (brain, heart/lungs, gut, liver, kidney, muscle, adipose tissue). Subcompartments were included as required to capture tissue dynamics (based on the capillary/interstitial diffusion resistance), and interactions between circulating insulin, glucose, and fatty acids were included with saturating hyperbolic tangent functions. This model also captured available literature data, and it provides a biologically-motivated structure from which additional characterization and validation studies can be designed as well as a platform for closed-loop algorithm synthesis and testing. 14:35 – 15:10 George Mitsis, National Technical University, Athens Nonparametric (kernel-based) nonlinear modeling of glucose-insulin regulation The dynamic relationship between insulin and glucose has been examined extensively using compartmental models, which usually assume the form of nonlinear differential equations. These models are based on prior assumptions about the underlying physiological mechanisms and are often combined with specific experimental protocols, such as glucose tolerance tests, to extract parameters of clinical importance. However, it remains questionable whether they accurately describe the dynamic effects of insulin on glucose (and vice versa) under more general operating conditions. With the advancement of continuous glucose sensor and programmable insulin micropump technology, the application of more general, data-driven approaches in modeling insulin-glucose interactions has become possible. Therefore, in the present work we will initially compare compartmental (differential equation) and Volterra (data-driven/nonparametric) models of the dynamic effects of variable infusions of insulin on blood glucose concentration in humans analytically. With respect to compartmental models, we consider the widely accepted ”minimal model”and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system. With respect to data-driven models, we consider the class of Volterra-type models that are estimated from input-output data, which describes a very broad class of dynamic nonlinear systems. We demonstrate the equivalence between the two approaches analytically and derive relations between the descriptors of the Volterra models, i.e., the Volterra kernels, in terms of the compartmental model parameters. We subsequently demonstrate the feasibility of obtaining accurate Volterra models from insulin-glucose utilizing both simulated data generated from the aforementioned compartmental models, as well as experimental data of frequently sampled spontaneous insulin and glucose variations in a fasting dog. The results corroborate the proposition that it may be preferable to obtain data-driven models in a realistic operating context, without resorting to the restrictive prior assumptions of model structure that are necessary for the compartmental (parametric) models. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models. 14:35 – 15:10 Michael Khoo, USC Modeling the interactions between metabolic and cardiorespiratory control dysfunction Obesity and insulin resistance are highly prevalent in subjects diagnosed with sleepdisordered breathing (SDB). One factor common to obesity, SDB and insulin resistance is sympathetic nervous system overactivity. Although the causal links among these factors are not well understood, it is likely that the vicious cycle of interplay among these factors predisposes to the emergence of ”metabolic syndrome”, a convergence of obesity, hypertension, insulin resistance and dyslipidemia that is appearing in epidemic proportions in the United States and other countries. In this talk, we will discuss the experimental and modeling studies currently underway in our laboratory, aimed at further elucidating the nature of the relationships among autonomic dysfunction, insulin resistance and severity of SDB in overweight subjects. To quantify autonomic dysfunction, we employ a closed-loop minimal model of cardiorespiratory control which has been tested extensively over a variety of conditions and subject groups over the past several years. In one of our ongoing studies, we estimate the parameters of the closed-loop model from human subjects under baseline conditions, and also under orthostatic stress and cold face stimulation. We subsequently determine the relationship of these model parameters to the parameters estimated from the Bergman minimal insulin-glucose model using data obtained from the frequently sampled intravenous glucose tolerance test performed on the same individuals. In a separate study, we are determining how autonomic function, as reflected in indices derived from heart rate variability and pulse transit time variability, in various sleep-wake stages is associated with measures of glucose metabolism based on the oral glucose tolerance test. Alongside these studies, we are also starting to explore the potential mechanisms for autonomic-metabolic interactions by developing a simulation model of metabolic control and linking it to a comprehensive model capable of simulating cardiorespiratory and sleep-wake control. 14:35 – 15:10 Jerry Batzel, University of Graz Parameter estimation issues in closed-loop modeling Physiological models can be of various complexity. Global models have been developed to summarize current knowledge, study interactions of various mechanisms, and consider causes of various clinical and health problems. Because of advances in computing power and numerical methods models of ever greater complexity can be studied. However, such models cannot usually be adapted to study the physiological features of a particular individual (or patient in the clinical setting) as the number of parameters to be estimated for the individual are too large given the available data. As new techniques for data measurement are developed the number of parameters that can be estimated should in principle increase but there is always a boundary where the modeler must decide how to simplify his or her model to match the level of system information contained in the available data. This leads necessarily to issues of model validation. An important conflict arises in modeling for clinical application because models need sufficient complexity to represent the system interactions directly or indirectly implicated in system dysfunction but in the clinical setting the ability to measure key states is either not possible or restricted by cost, time, and the desire for nonor minimally invasive testing procedures. This represents an important limiting factor for applications. The presentation will seek to familiarize the listener with current methods and computational techniques for validation of complex physiological models. We will examine physiological models and describe how to approach the parameter estimation process using several methods generally referred to as sensitivity analysis and exhibit how the information provided by these methods can aid in analyzing the problem of estimating key parameters. A special emphasis will be placed on the problem of only having access to data restricted to clinical sources. Applications will be drawn from modeling important control mechanisms of the human cardiovascular-respiratory system, glucose-insulin models, as well as anti-HIV treatment. Sensitivity analysis refers to the study of how variations in model parameters influences model output. This analysis can be used to provide insight into the parameter estimation process. Classical and generalized sensitivity analysis, as well as eigenvalue grouping, will be used to develop information on how the model-specific structure and limited data availability influence the parameter estimation process. Such information can improve the well-posedness as well as the numerical implementation of the estimation process. Such analysis can provide insight on the relevance of the data of various outputs for the estimation process and hence give ideas for improved experimental design to access the most important data. This is especially relevant for data collected in the clinical setting where cost and practicality are central concerns. For this talk, the constraint on the data is that it be collected only from nonor minimally invasive measurements in conjunction with specialized tests.