Estimation of insulin sensitivity in diabetic Göttingen Minipigs

In patients with type 1 diabetes mellitus, insulin sensitivity is a parameter which strongly affects insulin therapy. Due to its time-dependent variation, this parameter can improve the strategy for automatic closed-loop blood glucose control. The aim of this work is to estimate the insulin sensitivity of patients with type 1 diabetes mellitus based on measured blood glucose concentrations. For this, an Extended Kalman Filter is used, based on a simplified version of the well-known Sorensen model. The compartment model of Sorensen was adapted to the glucose metabolic behaviour in diabetic Göttingen Minipigs by means of experimental data and reduced by neglecting unobservable state variables. Here, the Extended Kalman Filter is designed for simultaneous state and parameter estimation of insulin sensitivity using the insulin infusion rate and the meal size as input signals, and measurements of blood glucose concentration as output signal. The performance of the Extended Kalman Filter was tested in in silico studies using the minipig model, and is analysed by comparing the output signal of the filter with measurement data from the animal trials.     

A modified index for control performance assessment

A control performance index which relates actual output variance to minimal achievable variance was first presented by Harris [T.J. Harris, Assessment of control loop performance, The Canadian Journal of Chemical Engineering 67 (1989) 856–861]. In the present paper, a modification of that index is applied. Instead of comparing to minimum variance control — which corresponds to placing all closed-loop poles in the origin — one pole is placed using either control design guidelines or additionally available process knowledge. Some possible choices of the free closed-loop pole are discussed. Based on this modified closed-loop system, a performance index can be calculated which relates actual output variance to the minimum achievable variance using the modified closed-loop system. It is shown that for the calculation of this index no other information apart from the measured process output and the time-delay is necessary. Furthermore, a method is presented which allows the assessment of the accuracy of the calculated index. The original Harris index and the proposed modified index are computed using data from industrial processes.     

Experimental validation of a glucose-insulin control model to stimulate patterns in glucose turnover

To verify a structured model of the glucose-insulin system, metabolic measurements were compared with model-based simulations in insulin-dependent diabetic dogs which had been previously identified in terms of model parameters. Glycaemia, glucosuria, plasma insulin, and the rates of appearance Ra and disappearance Rd of glucose (kinetics of double-labelled glucose, evaluated according to Steele's equation in its non-steady-state version) were observed under the following conditions, starting from normoglycaemia during glucose-controlled insulin infusion (GCII): (I) insulin withdrawal, (II) insulin withdrawal and glucose infusion, (III) constant i.v. infusion of glucose and insulin, (IV) glucose infusion during GCII. After fitting the patterns of glycaemia, simulations of the other state variables were accomplished, employing the individual model parameters, the preset experimental inputs, and the GCII control constants (test IV only). Under nearly all conditions, correspondence was excellent between measured and simulated data. There were, however, the following exceptions: incomplete representation by the model of kinetics in glucose utilisation after interruption of insulin supply, overestimation of glucosuria by the model in the presence of insulin. It is concluded that the model provides a reasonable representation of metabolic processes which are of importance in the treatment of insulin-dependent diabetes mellitus and that it might thus appropriately simulate the outcome of metabolic regimens.     

Identification of an integrated mathematical model of standard oral glucose tolerance test for characterization of insulin potentiation in health

Two new formulations, respectively denominated INT_M1 and INT_M2, of an integrated mathematical model to describe the glycemic and insulinemic responses to a 75 g oral glucose tolerance test (OGTT) are proposed and compared. The INT_M1 assumes a single compartment for the intestine and the derivative of a power exponential function for the gastric emptying rate, while, in the INT_M2, a nonlinear three-compartment system model is adopted to produce a more realistic, multiphase gastric emptying rate. Both models were implemented in a Matlab-based, two-step procedure for estimation of seven adjustable coefficients characterizing the gastric emptying rate and the incretin, insulin and glucose kinetics. Model behaviour was tested vs. mean plasma glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP), glucose and insulin measurements from two different laboratories, where glycemic profiles observed during a 75 g OGTT were matched in healthy subjects (HC1- and HC2-group, respectively) by means of an isoglycemic intravenous glucose (I-IVG) infusion. Under the hypothesis of an additive effect of GLP-1 and GIP on insulin potentiation, our results demonstrated a substantial equivalence of the two models in matching the data. Model parameter estimates showed to be suitable markers of differences observed in the OGTT and matched I-IVG responses from the HC1-group compared to the HC2-group. Model implementation in our two-step parameter estimation procedure enhances the possibility of a prospective application for individualization of the incretin effect in a single subject, when his/her data are plugged in.     

Model-based assessment of insulin sensitivity of glucose disposal and endogenous glucose production from double-tracer oral glucose tolerance test

A new mathematical model of short-term glucose regulation by insulin is proposed to exploit the oral glucose tolerance test (OGTT), which is commonly used for clinical diagnosis of glucose intolerance and diabetes. Contributions of endogenous and exogenous sources to measured plasma glucose concentrations have been separated by means of additional oral administration and constant intravenous infusion of glucose labeled with two different tracers. Twelve type 2 diabetic patients (7 males and 5 females) and 10 control subjects (5 males and 5 females) with normal glucose tolerance and matched body mass index (BMI) participated in this study. Blood samples for measurement of concentrations/activity of unlabeled and double-tracer glucose and insulin were collected every 15 min for 3 h following the oral glucose load. A minimal model combined with non-linear mixed-effects population parameter estimation has been devised to characterize group-average and between-patient variability of: (i) gastrointestinal glucose absorption; (ii) endogenous glucose production (EGP), and (iii) glucose disposal rate. Results indicate that insulin-independent glucose clearance does not vary significantly with gender or diabetic state and that the latter strongly affects, as expected, insulin-dependent clearance (insulin sensitivity). Inhibition of EGP, interpreted in terms of variations from basal of insulin concentrations, does not appear to be affected by diabetes but rather by BMI, i.e. by the degree of obesity. This study supports the utility of a minimal modelling approach, combined with population parameter estimation, to characterize glucose absorption, production and disposition during double-tracer OGTT experiments. The model provides a means for planning further experiments to validate the new hypothesis on the influence of individual factors, such as BMI and diabetes, on glucose appearance and disappearance, and for designing new simplified clinical tests.     

Data driven nonparametric identification and model based control of glucose-insulin process in type 1 diabetics

Closed loop control of glucose homeostasis via subcutaneous insulin infusion and continuous glucose monitoring system can give better living to a type 1 diabetic patient. This paper deals with the real time implementation of internal model control (IMC) of subcutaneous insulin infusion. The model based control is applied on the nonparametric model of the patient identified in real time from input–output data. Meal simulation model of the glucose-insulin system of type 1 diabetic patient based on the work of Dalla Man et. al. is considered. This model is constructed in hardware platform that acts as the virtual patient. The data-driven nonparametric model of the virtual patient is identified in real time by computing Volterra kernels. The kernels are solved up to second order using recursive least squares (RLS) algorithm with short memory length of M = 2. The validation results of the identified model output and the actual output have shown good fit in both simulation and real time environments. The frequency domain kernels are used in internal model control to generate insulin dosage. The control algorithm is developed in simulation and implemented in real time with hardware in loop on dSPACE platform. The closed loop system yields good meal disturbance rejection, less undershoots, settling time and more profoundly smaller requirement of insulin infusion as compared to the earlier reported data.     

A habituating blood glucose control strategy for the critically ill

In the intensive care unit patients benefit from being fed and from having well controlled glucose levels. Insulin and glucose infusion serves as manipulated inputs to regulate blood glucose, while glucose infusion serves as a sole nutritional input. In this paper, a model predictive control strategy, based on simultaneously manipulating glucose and insulin infusion, is developed to improve blood glucose regulation in intensive care unit patients. In the short term, glucose infusion is used for tighter glucose control, particularly for disturbance rejection, while, in the long-term (24 h period), glucose infusion is used to meet nutritional needs. The “habituating control” algorithm is proposed and tested against a model predictive control (MPC) strategy that only manipulates insulin. The simulation results indicate that the Habituating MPC strategy outperforms the single input–single output MPC by providing faster setpoint tracking and tighter glucose control for a patient population, and producing less glucose variability while rejecting disturbances in insulin infusion and insulin sensitivity.     

Weighting Restriction for Intravenous Insulin Delivery on T1DM Patient via $H_{infty}$ Control

A weighting restriction with frequency components is proposed for the insulin delivery on Type 1 Diabetics Mellitus (T1DM) towards the control of the blood glucose level. The weighting restriction is stated from a model of healthy subjects which includes a rate for insulin delivery. The frequency components are incorporated via a transfer function from the plasma glucose to the free-plasma insulin such that a H _infin-based controller is designed. In this way, the control synthesis involves the frequency components on which a healthy pancreas delivers insulin for the glucose homeostasis. In order to test controller performance, a dynamical model of an actuator is also included in the closed-loop system to add its effects in the closed-loop evaluation of the H _infin -based controller. The actuator is a pump to deliver of an insulin infusion according with the rate computed by the controller. Note that the contribution is particularly focused on T1DM; however, the inclusion of weighting restriction can be used also onto critical care conditions.     

A new general glucose homeostatic model using a proportional-integral-derivative controller

The glucose-insulin system is a challenging process to model due to the feedback mechanisms present, hence the implementation of a model-based approach to the system is an on-going and challenging research area. A new approach is proposed here which provides an effective way of characterising glycaemic regulation. The resulting model is built on the premise that there are three phases of insulin secretion, similar to those seen in a proportional-integral-derivative (PID) type controller used in engineering control problems. The model relates these three phases to a biological understanding of the system, as well as the logical premise that the homeostatic mechanisms will maintain very tight control of the system. It includes states for insulin, glucose, insulin action and a state to simulate an integral function of glucose. Structural identifiability analysis was performed on the model to determine whether a unique set of parameter values could be identified from the available observations, which should permit meaningful conclusions to be drawn from parameter estimation. Although two parameters--glucose production rate and the proportional control coefficient--were found to be unidentifiable, the former is not a concern as this is known to be impossible to measure without a tracer experiment, and the latter can be easily estimated from other means. Subsequent parameter estimation using Intravenous Glucose Tolerance Test (IVGTT) and hyperglycaemic clamp data was performed and subsequent model simulations have shown good agreement with respect to these real data.     

MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test

Insulin sensitivity and pancreatic responsivity are the two main factors controlling glucose tolerance. We have proposed a method for measuring these two factors, using computer analysis of a frequently-sampled intravenous glucose tolerance test (FSIGT). This 'minimal modelling approach' fits two mathematical models with FSIGT glucose and insulin data: one of glucose disappearance and one of insulin kinetics. MINMOD is the computer program which identifies the model parameters for each individual. A nonlinear least squares estimation technique is used, employing a gradient-type of estimation algorithm, and the first derivatives (not known analytically) are computed according to the 'sensitivity approach'. The program yields the parameter estimates and the precision of their estimation. From the model parameters, it is possible to extract four indices: SG, the ability of glucose per se to enhance its own disappearance at basal insulin, SI, the tissue insulin sensitivity index, phi 1, first phase pancreatic responsivity, and phi 2, second phase pancreatic responsivity. These four characteristic parameters have been shown to represent an integrated metabolic portrait of a single individual.     

A program to estimate insulin sensitivity and pancreatic responsivity from an IVGTT using the minimal modeling technique

A user-friendly program coded in PASCAL for the IBM PC has been developed to determine the etiology of impaired glucose tolerance using an intravenous glucose tolerance test (IVGTT). It makes use of the "minimal modeling technique," a method that has been shown to be adequate for the quantitative determination of insulin sensitivity and insulin resistance. Two models are used, the minimal model of glucose disappearance and the minimal model of insulin kinetics. The first model is described by two nonlinear ordinary differential equations (ODEs) which are solved numerically, and which yield the insulin sensitivity index SI. The second model is described by an ODE for which an explicit solution was obtained, and which yields the pancreatic responsivity parameters phi 1 and phi 2. The product SI.phi 2 can be used to segregate subjects into "good" and "low" tolerance types. The program provides best-fit plots along with numerical values of the parameters and their uncertainties, and requires little intervention from the user. The fact that it requires a noninvasive IVGTT as input and that it has been written for the ubiquitous IBM PC are added advantages.     

多变量时滞过程的解耦控制方法研究

针对工业过程中常见的多变量时滞输入输出系统,在改进的内模控制基础上提出了一种两自由度解耦控制方案,其优点是不仅使得标称系统各路输出响应之间完全解耦,而且能够实现系统给定值响应与负载干扰响应的解耦与在线调节和优化,采用加补偿项方法设计的两控制器矩阵能够保证系统具有较好的标称性能和鲁棒稳定性能.最后,通过仿真实例验证了该控制方案的有效性.     

A Run-to-Run Control Strategy to Adjust Basal Insulin Infusion Rates in Type 1 Diabetes

Maintaining good glycemic control is a daily challenge for people with type 1 diabetes. Insulin requirements are changing constantly due to many factors, such as levels of stress and physical activity. The basal insulin requirement also has a circadian rhythm, adding another level of complexity. Automating the adjustment of insulin dosing would result in improved glycemic control, as well as an improved quality of life by significantly reducing the burden on the patient. Building on our previous success of using run-to-run control for prandial insulin dosing (a strategy adapted from the chemical process industry), we show how this same framework can be used to adjust basal infusion profiles. We present a mathematical model of insulin–glucose dynamics which we augment in order to capture the circadian variation in insulin requirements. Using this model, we show that the run-to-run framework can also be successfully applied to adjust basal insulin dosing.     

A pharmacodynamic approach to optimizing insulin therapy

We have developed a program for simulation and optimization of insulin therapy in patients with insulin-dependent diabetes. The program, denoted GLUCOJECT, is based on a physiologic model of minimal complexity, which describes the pharmacokinetics of absorption and clearance of subcutaneous insulin and the dynamics of glucose utilization as dependent on both prevailing glucose and insulin levels. With self-monitored glucose values and insulin doses collected with one of several commercially available memory meters, GLUCOJECT reconstructs an average or 'typical' daily plasma glucose and insulin profile and displays them in a graph. The program then calculates the expected rate of glucose utilization, which permits calculation of the rate of glucose entry into plasma from both endogenous (hepatic) and exogenous (dietary) sources. In turn, this allows one to calculate an 'ideal' plasma insulin profile required to maintain a relatively constant 'ideal' plasma glucose level. GLUCOJECT can evaluate several different insulin regimens involving various combinations of short-, intermediate- and long-acting insulins, and select the one(s) most closely approximating the ideal or optimal insulin profile, using a least-squares criterion. For any optimized insulin regimen, GLUCOJECT calculates and displays the predicted time course of plasma glucose. These features make the program attractive as an educational tool for both patients and health care professionals and could potentially assist in the management of patients with insulin-dependent diabetes.     

Migrating from target-controlled infusion to closed-loop control in general anaesthesia

The target-controlled infusion (TCI) technique has been successfully and commercially used in clinical general anaesthesia with the intravenous anaesthetic agent propofol. The technique is based on a population pharmacokinetic model and is an open-loop control system. Closed-loop control requires a reliable and consistent signal for feedback utilisation. With all anaesthetic agents the somatosensory evoked potentials (SEP) have been shown to give increased latency as anaesthetic depth is increased. Using infusion rate and SEP response data from rats anaesthetised with propofol a mathematical model was derived to describe the anaesthetic process. This model was used as a design reference to develop a proportional integral (PI) closed-loop control system using SEP as the feedback measure. A serials of 10 trials were conducted to investigate the difference between continuous bolus injection and infusion, all under closed-loop control. The trials showed that the use of SEPs in closed-loop control of anaesthesia is feasible.     

Improved blood glucose control for critically ill subjects

For patients in intensive care units (ICUs), control of blood glucose level is an important factor in reducing serious complications and mortality. Standard protocols for glucose control in ICUs have been based on infrequent glucose measurements, look-up tables to determine the appropriate insulin infusion rates, and bedside administration of the insulin infusion by ICU staff. In this paper a new automatic control strategy is proposed based on frequent glucose measurements and a self-tuning control technique. During a short initial time period when manual glucose control is performed using a standard protocol, a simple dynamic model of the glucose-insulin system is identified in real time using recursive least squares. Then an adaptive PID controller is tuned, based on the model parameters, and the controller is turned on. A simulation study based on detailed physiological models of the glucose-insulin dynamics demonstrates that the proposed control strategy performs better than standard protocols for insulin infusion.     

Robust hand-eye calibration of 2D laser sensors using a single-plane calibration artefact

When a vision sensor is used in conjunction with a robot, hand-eye calibration is necessary to determine the accurate position of the sensor relative to the robot. This is necessary to allow data from the vision sensor to be defined in the robot's global coordinate system. For 2D laser line sensors hand-eye calibration is a challenging process because they only collect data in two dimensions. This leads to the use of complex calibration artefacts and requires multiple measurements be collected, using a range of robot positions. This paper presents a simple and robust hand-eye calibration strategy that requires minimal user interaction and makes use of a single planar calibration artefact. A significant benefit of the strategy is that it uses a low-cost, simple and easily manufactured artefact; however, the lower complexity can lead to lower variation in calibration data. In order to achieve a robust hand-eye calibration using this artefact, the impact of robot positioning strategies is considered to maintain variation. A theoretical basis for the necessary sources of input variation is defined by a mathematical analysis of the system of equations for the calibration process. From this, a novel strategy is specified to maximize data variation by using a circular array of target scan lines to define a full set of required robot positions. A simulation approach is used to further investigate and optimise the impact of robot position on the calibration process, and the resulting optimal robot positions are then experimentally validated for a real robot mounted laser line sensor. Using the proposed optimum method, a semi-automatic calibration process, which requires only four manually scanned lines, is defined and experimentally demonstrated.     

Neural predictive controller for closed-loop control of glucose using the subcutaneous route: A simulation study

The objective of this study was to develop and evaluate a strategy for closed-loop control of glucose using subcutaneous (s.c.) glucose measurement and s.c. infusion of monomeric insulin analogues. The method was based on off-line identification of the glucoregulatory system using neural networks and a nonlinear model predictive controller. Numerical studies on system identification and closed-loop control of glucose were carried out using a comprehensive model of glucose regulation. The proposed control strategy was robust against noise and time delays, and enabled stable control also for slow time variations of the controlled process. In conclusion, closed-loop control of glucose is feasible using the s.c. route and a neural predictive controller.     

A generalised maintenance policy with age-dependent minimal repair cost for a system subject to shocks under periodic overhaul

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur, the system has two types of failures: type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by overhaul or replacement. The cost of minimal repair depends on age. A system is overhauled when the occurrence of a type 2 failure or at age T, whichever occurs first. At the N-th overhaul, the system is replaced rather than overhauled. A maintenance policy for determining optimal number of overhauls and optimal interval between overhauls which incorporate minimal repairs, overhauls and replacement is proposed. Under such a policy, an approach which using the concept of virtual age is adopted. It is shown that there exists a unique optimal policy which minimises the expected cost rate under certain conditions. Various cases are considered.