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.     

Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes

Current insulin therapy for patients with type 1 diabetes often results in high variability in blood glucose concentrations and may cause hyperglycemic/hypoglycemic episodes. Closing the glucose control loop with a fully automated electro-mechanical pancreas will improve the quality of life for insulin-dependent patients. An adaptive control algorithm is proposed to keep glucose concentrations within normoglycemic range and dynamically respond to glycemic challenges. A model-based control strategy is used to calculate the required insulin infusion rate, while the model parameters are recursively tuned. The algorithm handles delays associated with insulin absorption, time-lag between subcutaneous and blood glucose concentrations, and variations in inter/intra-subject glucose–insulin dynamics. Simulation results for simultaneous meal and physiological disturbances are demonstrated for subcutaneous insulin infusion.     

Combining statistical, rule-based, and physiologic model-based methods to assist in the management of diabetes mellitus

Self-monitoring of capillary blood glucose is used by most patients with insulin-dependent diabetes mellitus as a means of assessing metabolic control. Therapeutic interventions are based on retrospective analysis of glycemic response to various factors, with insulin and diet playing the key roles. We describe a computer system being developed for intelligent automated analysis and interpretation of data relevant to glycemic control. CADMO (Computer-Assisted Diabetes Monitor) is intended to assist health care professionals with the management of patients with insulin-dependent diabetes. It takes as input glucose values and insulin doses collected via a memory meter by the patient over a period of several weeks. Rule-based logic, statistical methods, and a physiologic model of insulin pharmacokinetics and glucose dynamics are used to help detect meaningful patterns and trends in glucose and insulin data and to suggest approaches for optimizing insulin regimens.     

Continuous-time interval model identification of blood glucose dynamics for type 1 diabetes

While good physiological models of the glucose metabolism in type 1 diabetic patients are well known, their parameterisation is difficult. The high intra-patient variability observed is a further major obstacle. This holds for data-based models too, so that no good patient-specific models are available. Against this background, this paper proposes the use of interval models to cover the different metabolic conditions. The control-oriented models contain a carbohydrate and insulin sensitivity factor to be used for insulin bolus calculators directly. Available clinical measurements were sampled on an irregular schedule which prompts the use of continuous-time identification, also for the direct estimation of the clinically interpretable factors mentioned above. An identification method is derived and applied to real data from 28 diabetic patients. Model estimation was done on a clinical data-set, whereas validation results shown were done on an out-of-clinic, everyday life data-set. The results show that the interval model approach allows a much more regular estimation of the parameters and avoids physiologically incompatible parameter estimates.     

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 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.     

Volumetric quantification of the gastric emptying: computer-based method for generation of volumetric index from fluoroscopic images

We developed an automated software-based procedure for estimation of the volume variation of the stomach using videofluoroscopic analysis of the gastric emptying. We used radiological images with postero-anterior incidence of eight healthy volunteers and in vitro experimental tests, with different volumes and concentrations of the contrast medium. This computational method generates an index that measures, in the three dimensions, the dynamic behaviour of gastric emptying. Using adequate contrast concentration (barium sulphate solution), it is possible to determine volume behaviour from density variations. This software can automate this computation, facilitating the amount of work, avoiding mistakes and improving reproducibility.     

Structural identifiability and indistinguishability analyses of the Minimal Model and a Euglycemic Hyperinsulinemic Clamp model for glucose-insulin dynamics

Many mathematical models have been developed to describe glucose-insulin kinetics as a means of analysing the effective control of diabetes. This paper concentrates on the structural identifiability analysis of certain well-established mathematical models that have been developed to characterise glucose-insulin kinetics under different experimental scenarios. Such analysis is a pre-requisite to experiment design and parameter estimation and is applied for the first time to these models with the specific structures considered. The analysis is applied to a basic (original) form of the Minimal Model (MM) using the Taylor Series approach and a now well-accepted extended form of the MM by application of the Taylor Series approach and a form of the Similarity Transformation approach. Due to the established inappropriate nature of the MM with regard to glucose clamping experiments an alternative model describing the glucose-insulin dynamics during a Euglycemic Hyperinsulinemic Clamp (EIC) experiment was considered. Structural identifiability analysis of the EIC model is also performed using the Taylor Series approach and shows that, with glucose infusion as input alone, the model is structurally globally identifiable. Additional analysis demonstrates that the two different model forms are structurally distinguishable for observation of both glucose and insulin.     

Fuzzy filter for state estimation of a glucoregulatory system

A filter based on fuzzy logic for state estimation of a glucoregulatory system is presented. A published non-linear model for the dynamics of glucose and its hormonal control including a single glucose compartment, five insulin compartments and a glucagon compartment was used for simulation. The simulated data were corrupted by an additive white noise with zero mean and a coefficient of variation (CV) of between 2 and 20% and then submitted to the state estimation procedure using a fuzzy filter (FF). The performance of the FF was compared with an extended Kalman filter (EKF) for state estimation. Both the FF and the EKF were evaluated in the following cases: (a) five state variables are measurable; three plasma variables are measurable; only plasma glucose is measurable; (b) for different measurement noise levels (CV of 2–20%); and (c) a mismatch between the glucoregulatory system and the given mathematical model (uncertain or approximate model). In contrast to the FF, in the case of approximate model of the glucose system, the EKF failed to achieve useful state estimation. Moreover, the performance of the FF was independent of the noise level. In conclusion, the FF approach is a viable alternative for state estimation in a noisy environment and with an uncertain mathematical model of the glucoregulatory system.     

Bayesian function learning using MCMC methods

The paper deals with the problem of reconstructing a continuous 1D function from discrete noisy samples. The measurements may also be indirect in the sense that the samples may be the output of a linear operator applied to the function. Bayesian estimation provides a unified treatment of this class of problems. We show that a rigorous Bayesian solution can be efficiently implemented by resorting to a Markov chain Monte Carlo (MCMC) simulation scheme. In particular, we discuss how the structure of the problem can be exploited in order to improve the computational and convergence performances. The effectiveness of the proposed scheme is demonstrated on two classical benchmark problems as well as on the analysis of IVGTT (IntraVenous glucose tolerance test) data, a complex identification-deconvolution problem concerning the estimation of the insulin secretion rate following the administration of an intravenous glucose injection     

Nonlinear glucose–insulin control considering delays—Part II: Control algorithm

The closed loop control of blood glucose levels in a nonlinear glucose–insulin regulatory system is considered in this paper. Based on the subcutaneous glucose sensor readings, a control algorithm is designed and implemented. A mathematical model characterizing the ultradian oscillatory nature of the glucose–insulin regulatory system of diabetic patients is considered and an estimation based model predictive control scheme with physiological and actuator constraints is implemented. An in silico preclinical testing is done to corroborate the control algorithm using the UVa/Padova virtual patient software.     

基于胰岛素基础率估计的人工胰腺系统自抗扰控制

胰岛素基础率是人工胰腺系统实现人体血糖闭环控制的基准, 但该变量在临床治疗中难以准确确定. 针对这一问题, 本文设计了一种基于胰岛素基础率动态估计的人工胰腺自抗扰控制方法, 通过扩张状态观测器(Extended state observer, ESO)实时估计血糖代谢过程中的内部与外界干扰, 构建具备参数自适应能力的反馈控制律和胰岛素注射安全约束, 实现血糖闭环调控能力的有效改善. 在此基础上, 本文设计了基于移动设备和蓝牙模块的人工胰腺软件系统, 并通过美国食品药品监督管理局(Food and Drug Administration, FDA)接受的UVA/Padova T1DM仿真平台完成算法的比较仿真与功能测试. 本文的工作将为后续人工胰腺临床试验的开展提供方法基础和技术支持, 也为我国糖尿病患者血糖管理的改善提供精准医学治疗手段.     

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.     

Stochastic modelling of insulin sensitivity and adaptive glycemic control for critical care

Targeted, tight model-based glycemic control in critical care patients that can reduce mortality 18-45% is enabled by prediction of insulin sensitivity, S(I). However, this parameter can vary significantly over a given hour in the critically ill as their condition evolves. A stochastic model of S(I) variability is constructed using data from 165 critical care patients. Given S(I) for an hour, the stochastic model returns the probability density function of S(I) for the next hour. Consequently, the glycemic distribution following a known intervention can be derived, enabling pre-determined likelihoods of the result and more accurate control. Cross validation of the S(I) variability model shows that 86.6% of the blood glucose measurements are within the 0.90 probability interval, and 54.0% are within the interquartile interval. "Virtual Patients" with S(I) behaving to the overall S(I) variability model achieved similar predictive performance in simulated trials (86.8% and 45.7%). Finally, adaptive control method incorporating S(I) variability is shown to produce improved glycemic control in simulated trials compared to current clinical results. The validated stochastic model and methods provide a platform for developing advanced glycemic control methods addressing critical care variability.     

Modeling the glucose regulatory system in extreme preterm infants

Background

Premature infants represent a significant proportion of the neonatal intensive care population. Blood glucose homeostasis in this group is often disturbed by immaturity of endogenous regulatory systems and the stress of their condition. Hypo- and hyperglycemia are frequently reported in very low birth weight infants, and more mature infants often experience low levels of glycemia. A model capturing the unique fundamental dynamics of the neonatal glucose regulatory system could be used to develop better blood glucose control methods.

Methods

A metabolic system model is adapted from adult critical care to the unique physiological case of the neonate. Integral-based fitting methods were used to identify time-varying insulin sensitivity and non-insulin mediated glucose uptake profiles. The clinically important predictive ability of the model was assessed by assuming insulin sensitivity was constant over prediction intervals of 1, 2 and 4 h forward and comparing model-simulated versus actual clinical glucose values for all recorded interventions. The clinical data included 1091 glucose measurements over 3567 total patient hours, along with all associated insulin and nutritional infusion data, for N = 25 total cases. Ethics approval was obtained from the Upper South A Regional Ethics Committee for this study.

Results

The identified model had a median absolute percentage error of 2.4% [IQR: 0.9-4.8%] between model-fitted and clinical glucose values. Median absolute prediction errors at 1-, 2- and 4-h intervals were 5.2% [IQR: 2.5-10.3%], 9.4% [IQR: 4.5-18.4%] and 13.6% [IQR: 6.3-27.6%] respectively.

Conclusions

The model accurately captures and predicts the fundamental dynamic behaviors of the neonatal metabolism well enough for effective clinical decision support in glycemic control. The adaptation from adult to a neonatal case is based on the data from the literature. Low prediction errors and very low fitting errors indicate that the fundamental dynamics of glucose metabolism in both premature neonates and critical care adults can be described by similar mathematical models.     

First pilot trial of the STAR-Liege protocol for tight glycemic control in critically ill patients

Tight glycemic control (TGC) has shown benefits in ICU patients, but been difficult to achieve consistently due to inter- and intra- patient variability that requires more adaptive, patient-specific solutions. STAR (Stochastic TARgeted) is a flexible model-based TGC framework accounting for patient variability with a stochastically derived maximum 5% risk of blood glucose (BG) below 72mg/dL. This research describes the first clinical pilot trial of the STAR approach and the post-trial analysis of the models and methods that underpin the protocol. The STAR framework works with clinically specified targets and intervention guidelines. The clinically specified glycemic target was 125mg/dL. Each trial was 24h with BG measured 1-2hourly. Two-hourly measurement was used when BG was between 110-135mg/dL for 3h. In the STAR approach, each intervention leads to a predicted BG level and outcome range (5-95th percentile) based on a stochastic model of metabolic patient variability. Carbohydrate intake (all sources) was monitored, but not changed from clinical settings except to prevent BG<100mg/dL when no insulin was given. Insulin infusion rates were limited (6U/h maximum), with limited increases based on current infusion rate (0.5-2.0U/h), making this use of the STAR framework an insulin-only TGC approach. Approval was granted by the Ethics Committee of the Medical Faculty of the University of Liege (Liege, Belgium). Nine patient trials were undertaken after obtaining informed consent. There were 205 measurements over all 9 trials. Median [IQR] per-patient results were: BG: 138.5 [130.6-146.0]mg/dL; carbohydrate administered: 2-11g/h; median insulin:1.3 [0.9-2.4]U/h with a maximum of 6.0 [4.7-6.0]U/h. Median [IQR] time in the desired 110-140mg/dL band was: 50.0 [31.2-54.2]%. Median model prediction errors ranged: 10-18%, with larger errors due to small meals and other clinical events. The minimum BG was 63mg/dL and no other measurement was below 72mg/dL, so only 1 measurement (0.5%) was below the 5% guaranteed minimum risk level. Post-trial analysis showed that patients were more variable than predicted by the stochastic model used for control, resulting in some of the prediction errors seen. Analysis and (validated) virtual trial re-simulating the clinical trial using stochastic models relevant to the patient's particular day of ICU stay were seen to be more accurate in capturing the observed variability. This analysis indicated that equivalent control and safety could be obtained with similar or lower glycemic variability in control using more specific stochastic models. STAR effectively controlled all patients to target. Observed patient variability in response to insulin and thus prediction errors were higher than expected, likely due to the recent insult of cardiac surgery or a major cardiac event, and their immediate recovery. STAR effectively managed this variability with no hypoglycemia. Improved stochastic models will be used to prospectively test these outcomes in further ongoing clinical pilot trials in this and other units.     

多孔介质孔隙模型及其应用——毛细管束模型

在多孔介质中许多物理化学行为均与其自身的孔隙结构构型密切相关 ,建立一种切实可行的孔隙模型将会对研究材料和化工过程多孔介质提供很大的帮助。毛细管模型是一种较为简单的实用孔隙模型 ,它可以通过使用毛细管压对多孔介质的浸渗和排空情况进行计算 ,也可以用于对多孔介质中的浸渗和排空过程进行定性的解释。针对在研项目 ,对毛细管束模型情况做一评述     

基于UWB的无线传感器网络中的两步TOA估计法

为了设计一种以较小运算量获得较高测距精度的TOA(time of arrival)估计算法以适合节点运算能力有限的UWB(ultra wideband)无线传感器网络,提出了一种结合能量检测与匹配滤波的两步TOA估计方法.分析了该方法的工作原理,指出了第1步中DP(direct path)块检测成功率及第2步中匹配滤波门限因子设置的重要性.通过仿真对影响DP块检测成功率的两个因素,即DP块检测算法的选用和能量积分周期的设置进行了讨论.提出了依据能量采样序列中DP块与最小块比值DMR(DP to minimum energy sample ratio)动态设置匹配滤波门限因子的思想,并为其建立了数学模型.仿真结果表明,两步TOA估计方法在运算量比单一的基于匹配滤波的相干算法小很多的情况下,获得了比单一的基于能量检测的非相干方法更好的TOA估计性能,从而更适合应用于有低复杂度、低能耗设计需求的传感器节点中.