Mathematical modeling and analysis of insulin clearance in vivo

Background: Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. Results: We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. The model describes renal and hepatic insulin degradation, pancreatic insulin secretion and nonspecific insulin binding in the liver. Hepatic insulin receptor activation by insulin binding, receptor internalization and autophosphorylation is explicitly included in the model. We present a detailed mathematical analysis of insulin degradation and insulin clearance. Stationary model analysis shows that degradation rates, relative contributions of the different tissues to total insulin degradation and insulin clearance highly depend on the insulin concentration. Conclusions: This study provides a detailed dynamic model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. Experimental data sets from literature are used for the model validation. We show that essential dynamic and stationary characteristics of insulin degradation are nonlinear and depend on the actual insulin concentration. © 2008 Koschorreck and Gilles; licensee BioMed Central Ltd. [accessed July 4, 2008

In silico Models of Alcohol Dependence and Treatment

In this paper we view alcohol dependence and the response to treatment as a recurrent bio-behavioral process developing in time and propose formal models of this process combining behavior and biology in silico. The behavioral components of alcohol dependence and treatment are formally described by a stochastic process of human behavior, which serves as an event generator challenging the metabolic system. The biological component is driven by the biochemistry of alcohol intoxication described by deterministic models of ethanol pharmacodynamics and pharmacokinetics to enable simulation of drinking addiction in humans. Derived from the known physiology of ethanol and the literature of both ethanol intoxication and ethanol absorption, the different models are distilled into a minimal model (as simple as the complexity of the data allows) that can represent any specific patient. We use these modeling and simulation techniques to explain responses to placebo and ondansetron treatment observed in clinical studies. Specifically, the response to placebo was explained by a reduction of the probability of environmental reinforcement, while the effect of ondansetron was explained by a gradual decline in the degree of ethanol-induced neuromodulation. Further, we use in silico experiments to study critical transitions in blood alcohol levels after specific average number of drinks per day, and propose the existence of two critical thresholds in the human – one at 5 and another at 11 drinks/day – at which the system shifts from stable to critical and to super critical state indicating a state of alcohol addiction. The advantages of such a model-based investigation are that (1) the process of instigation of alcohol dependence and its treatment can be deconstructed into meaningful steps, which allow for individualized treatment tailoring, and (2) physiology and behavior can be quantified in different (animal or human) studies and then the results can be integrated in silico

Bariatric surgery improves postprandial VLDL kinetics and restores insulin mediated regulation of hepatic VLDL production

Dyslipidemia in obesity results from excessive production and impaired clearance of triglyceride-rich (TG-rich) lipoproteins, which are particularly pronounced in the postprandial state. Here, we investigated the impact of Roux-en-Y gastric bypass (RYGB) surgery on postprandial VLDL1 and VLDL2 apoB and TG kinetics and their relationship with insulin-responsiveness indices. Morbidly obese patients without diabetes who were scheduled for RYGB surgery (n = 24) underwent a lipoprotein kinetics study during a mixed-meal test and a hyperinsulinemic-euglycemic clamp study before the surgery and 1 year later. A physiologically based computational model was developed to investigate the impact of RYGB surgery and plasma insulin on postprandial VLDL kinetics. After the surgery, VLDL1 apoB and TG production rates were significantly decreased, whereas VLDL2 apoB and TG production rates remained unchanged. The TG catabolic rate was increased in both VLDL1 and VLDL2 fractions, but only the VLDL2 apoB catabolic rate tended to increase. Furthermore, postsurgery VLDL1 apoB and TG production rates, but not those of VLDL2, were positively correlated with insulin resistance. Insulin-mediated stimulation of peripheral lipoprotein lipolysis was also improved after the surgery. In summary, RYGB resulted in reduced hepatic VLDL1 production that correlated with reduced insulin resistance, elevated VLDL2 clearance, and improved insulin sensitivity in lipoprotein lipolysis pathways.</p

In vivo animal models for drug delivery across the lung mucosal barrier.

Over recent years the research focus within the field of respiratory drug delivery has broadened to include a wide range of potential applications for inhalation by delivering drugs not just onto the lung mucosa but across it. The range of drugs being assessed is broad and includes both current and novel therapies and there are a growing number of additives that appear capable of enhancing systemic absorption. Comprehensive characterisation of drug delivery to the lungs is a complex task involving the determination of delivered, deposited and (for systemically-targeted drugs) absorbed dose. As it is difficult to simulate in vitro, in vivo whole animal models are still key to inhaled drug development. Because of the anatomical complexities and interspecies differences in the lungs, the appropriate choice of species and drug delivery method is vital during study design. New delivery devices designed specifically for animal studies as well as more sophisticated methods to determine drug deposition and absorption after inhalation are improving the information derived from these studies

Mathematical studies of the glucose-insulin regulatory system models.

Three dynamic models are proposed to study the mechanism of glucose-insulin regulatory system and the possible causes of diabetes mellitus. The progression of diabetes comes along with the apoptosis of pancreatic beta-cells. A dynamical system model is formulated based on physiology and studied by geometric singular perturbation theory. The analytical studies reveal rich analytical features, such as persistence of solutions, Hopf bifurcation and backward bifurcation, while numerical studies successfully fit available longitudinal T2DM data of Pima Indian tribe. These studies together not only validate our model, but also point out key intrinsic factors leading to the development of T2DM. We found that the intermittent rests of beta-cells in insulin secretion are essential for the cells to survive through the observation of the existence of a limit cycle. A delay differential equation model for IVGTT is also studied thoroughly to determine the range of time delay and the globally asymptotic stability by Liapunov function. The third kinetic model aims to investigate the scaling effect of local insulin in islet on proliferation and apoptosis of beta-cells. It is revealed that the local concentration of monomeric insulin within the islet is in the biologist defined picomolar ‘sweet spot’ range of insulin doses, which activate the insulin receptors and have the most potent effects on beta-cells in vitro

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with [Formula: see text]-cells and the other with no [Formula: see text]-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no [Formula: see text]-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with [Formula: see text]-cells required more parameters to match the data and we fitted the [Formula: see text]-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of [Formula: see text] , and a difference in BIC of [Formula: see text] for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from [Formula: see text] to [Formula: see text]. Our results suggest that the model without [Formula: see text]-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes