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.     

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 mathematical insulin-secretion model and its validation in isolated rat pancreatic islets perifusion

A mathematical insulin-secretion model was constructed by analyzing the glucose-induced insulin secretion using a control theory. To validate the model, experimental data obtained in the isolated rat pancreatic islet perifusion system were compared with the simulation results. The simulation study of the model was found to fit quite well to insulin responses under various experimental conditions. A glucose-induced insulin secretion from pancreatic islets' β cell was found to be expressed as a function of proportional plus derivative response to glucose input with the first order time lag. And the negative rate of change in glucose concentration was found to suppress insulin secretion to the extent of the negative stimuli, regardless of glucose concentration. This model would be useful as a research tool for analysis of physiological significance of insulin secretory dynamics and clinical investigation of insulin secretion.     

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.     

Computer Simulation and Data Analysis of Effector-Target Interactions: The Extraction of Binding Parameters from Effector and Target Conjugate Frequencies Data by Using Linear and Nonlinear Data-Fitting Transformations

Binding isotherms for effector-target conjugation when effector conjugate frequencies are measured by holding constant the number of effector cells and by varying the number of target cells are characterized by two parameters, the maximum effector conjugate frequency, α_max, and γ, which is related to the dissociation constant of the conjugates formed,K_d. The suitability of four linear transformations of these binding isotherms, as well as nonlinear data-fitting techniques, to provide estimates of α_maxand γ is discussed. The strength and weakness of these procedures were investigated by calculating α_maxand γ from different sets of 100 or 500 replicate “experiments,” which were generated by using an algorithm that provides noise contributions to the conjugate frequencies with gaussian distributed errors. Both unweighted and weighted data points were used in these calculations. A similar analysis can also be performed for binding isotherms in which target conjugate frequencies are measured at different values of effector cells by holding constant the number of target cells. In this case, the binding isotherms are characterized by two parameters, the maximum target conjugate frequency, β_max, and δ, which is also related toK_d. The results obtained demonstrate that if the experimental conditions are chosen properly, linear transformations and nonlinear fitting techniques provide reliable estimates for the binding parameters. Not all procedures, however, provide estimates with the same accuracy, and special emphasis to this fact must be given if the binding assays are performed at low values of the number of effector cells.     

自主移动小车轨迹跟踪的参数优化及仿真研究

控制律中参数的选取在很大程度上影响着自主移动小车的轨迹跟踪精度,但很少有人考虑参数的优化取值问题。首先,该文将轨迹跟踪控制变量转换至小车车轮上以确保控制能在实际系统中实现;然后,用遗传算法对控制律中的参数进行优化设计,并用MATLAB进行了仿真研究。仿真结果表明：控制参数的选取对自主移动小车的轨迹跟踪精度影响很大;相同的控制参数对在不同的自主移动小车初始位姿下的轨迹跟踪控制效果不同;通过优化控制参数以提高自主移动小车的轨迹跟踪精度是可行与有效的。     

A computer program for analyzing enzyme kinetic data using graphical display and statistical analysis

A computer program, PENNZYME (M. C. Kohn, L. E. Menten, and D. Garfinkel, Comput. Biomed. Res. 12, 461, 1979), that fits trial rate laws to enzyme and transport steady-state kinetic data by nonlinear regression has been enhanced. The new version includes a set of mnemonic commands which can be displayed in a menu at the user's option. Graphic displays of measured data and computed curves, as well as deviations between them (residual plots) have been added to aid the user in determining if a model is free of bias or systematic error. Other features include the ability to display the variance-covariance matrix of the parameters, to hold individual parameters constant during an optimization, and to optimize error models for the experimental data by the extended-least-squares technique.     

Prediction of postprandial blood glucose under uncertainty and intra-patient variability in type 1 diabetes: A comparative study of three interval models

The behavior of three insulin action and glucose kinetics models was assessed for an insulin therapy regime in the presence of patient variability. For this purpose, postprandial glucose in patients with type 1 diabetes was predicted by considering intra- and inter-patient variability using modal interval analysis. Equations to achieve optimal prediction are presented for models 1, 2 and 3, which are of increasing complexity. The model parameters were adjusted to reflect the "same" patient in the presence of variability. The glucose response envelope for model 1, the simplest insulin-glucose model assessed, included the responses of the other two models when a good fit of the model parameters was achieved. Thus, under variability, simple glucose-insulin models may be sufficient to describe patient dynamics in most situations.     

Independent cohort cross-validation of the real-time DISTq estimation of insulin sensitivity

Insulin sensitivity (SI) is useful in the diagnosis, screening and treatment of diabetes. However, most current tests cannot provide an accurate, immediate or real-time estimate. The DISTq method does not require insulin or C-peptide assays like most SI tests, thus enabling real-time, low-cost SI estimation. The method uses a posteriori parameter estimations in the absence of insulin or C-peptide assays to simulate accurate, patient-specific, insulin concentrations that enable SI identification.Mathematical functions for the a posteriori parameter estimates were generated using data from 46 fully sampled DIST tests (glucose, insulin and C-peptide). SI values found using the DISTq from the 46 test pilot cohort and a second independent 218 test cohort correlated R = 0.890 and R = 0.825, respectively, to the fully sampled (including insulin and C-peptide assays) DIST SI metrics. When the a posteriori insulin estimation functions were derived using the second cohort, correlations for the pilot and second cohorts reduced to 0.765 and 0.818, respectively.These results show accurate SI estimation is possible in the absence of insulin or C-peptide assays using the proposed method. Such estimates may only need to be generated once and then used repeatedly in the future for isolated cohorts. The reduced correlation using the second cohort was due to this cohort's bias towards low SI insulin resistant subjects, limiting the data set's ability to generalise over a wider range. All the correlations remain high enough for the DISTq to be a useful test for a number of clinical applications. The unique real-time results can be generated within minutes of testing as no insulin and C-peptide assays are required and may enable new clinical applications.     

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.     

面向智能血糖管理的餐前胰岛素剂量贝叶斯学习优化方法

餐前胰岛素剂量精准决策是改善糖尿病患者血糖管理的关键. 临床治疗中胰岛素剂量调整一般在较短时间内完成, 具有典型的小样本特征; 数据驱动建模在该情形下无法准确学习患者餐后血糖代谢规律, 难以确保胰岛素剂量的安全和有效决策. 针对这一问题, 设计一种临床经验辅助的餐前胰岛素剂量自适应优化决策框架, 构建高斯过程血糖预测模型和模型有效性在线评估机制, 提出基于历史剂量和临床经验决策约束的贝叶斯优化方法, 实现小样本下餐后血糖轨迹的安全预测和餐前胰岛素注射剂量的优化决策. 该方法的安全性和有效性通过美国食品药品监督管理局接受的UVA/Padova T1DM平台测试结果和1型糖尿病患者实际临床数据决策结果充分验证. 可为餐前胰岛素剂量智能决策及临床试验提供方法基础和技术支持, 也为中国糖尿病患者血糖管理水平的有效改善, 提供了精准医学治疗手段.     

Analysis of the identification of closed-loop systems using least-squares methods

This paper presents theory and results concerning the analysis of the identification of closed-loop systems using least-squares methods. The least-squares technique is applied in its normal form and in a modified version developed to cope with the bias problem. The analysis has been established following a mathematical investigation of the problem, and by simulation of different identification experiments applied to different structures of closed-loop systems.

The results derived from this analysis show the conditions under which the identifiability of the open-loop process can be ensured, considering different situations such as whether or not there is noise present at the system output and whether or not external signals are used to perform the identification experiments.

Practical experiments of closed-loop identification on a micromachine system in use in the Department of Electrical Engineering of the University of Manchester are also described. Results for different experimental conditions are presented through graphs showing both the plant and the identified model outputs for the same sequence of sampled input signals.     

Worst-case space and time complexity of recursive procedures

The purpose of this paper is to show that recursive procedures can be used for implementing real-time applications without harm, if a few conditions are met. These conditions ensure that upper bounds for space and time requirements can be derived at compile time. Moreover they are simple enough such that many important recursive algorithms can be implemented, for example Mergesort or recursive tree-traversal algorithms.In addition, our approach allows for concentrating on essential properties of the parameter space during space and time analysis. This is done by morphisms that transfer important properties from the original parameter space to simpler ones, which results in simpler formulas of space and time estimates.Supported by the Austrian Science Foundation (FWF) under grant P10188-MAT.A preliminary version of this paper has been presented at the 7th Euromicro Workshop on Real-Time Systems (Blieberger and Lieger, 1995).     

SIAM: Statistics information access method

This paper outlines a new data access method for statistical information. When statistical data is organized using this access method, statistical parametric estimates can be processed asymptotically with respect to time, i.e. the precision of the estimates increases asymptotically with increase in processing time. This structure also enables the estimation of statistical parameters for range-type queries. Estimating the mean value and the second moment of the values of an attribute using SIAM is illustrated. Expressions for precision of the estimates, using up to a certain level of the SIAM index structure, are derived. SIAM structures have been extended to bivariate situation, for calculating covariances. Sampling techniques bases on SIAM organization has been discussed. Performance for computing statistics from SIAM structures has been compared with the present data access methods.     

Matlab在化工数据及模型参数拟合中的应用

在化工研究中,经常需要将实验数据拟合为数学模型,以定量描述过程或现象自变量与因变量之间的关系,模型参数的求取,一般采用最小二乘法。本文介绍了Matlab语言中利用最小二乘法以求取模型参数的几种功能函数及使用方法,通过举例对单变量曲线拟合、多变量曲线拟合及微分形式拟合进行了介绍,说明Matlab语言可拟合大部分实验数据,达到节约数据处理的时间,提高模型参数精度的目的。     

Phases of functional, near-normoglycaemic insulin substitution: what are computers good for in the rehabilitation process in type I (insulin-dependent) diabetes mellitus?

We have divided the rehabilitation process in patients with insulin-dependent diabetes mellitus into the following four phases. The basic phase, the so-called 'phase 0', provides information about literature, different strategies of treatment and introduces the use of regular insulin as well as blood sugar self-monitoring. During 'phase 1' (i.e. 'diabetes education common sense') all the initial information from 'phase 0' will be used practically and discussed in depth. After the patient's actual insulin need (U/24 h) has been estimated, initial algorithms for functional insulin use can be defined. And this is the turning point to 'phase 2' of the group rehabilitation process, the so-called education in functional insulin use. Initial algorithms should be understood as a preliminary answer to the patient's questions, 'What is my basal insulin need?', 'How much insulin do I need for a particular amount of carbohydrates?', and 'What is the hypothetical response of my blood glucose to a particular amount of insulin?'. These algorithms are going to be used and optimised now by the patient (under the supervision of the physician) during the so-called 'insulin games' (fasting or 24 h, experimental violation of traditional dietary rules, etc.) to demonstrate (1) how to influence actual glycaemia through immediate correction of blood sugar off blood sugar target (primary adjustment of insulin dosing), and (2) how to optimise algorithms for insulin use (secondary insulin adjustment) in future conditions of different insulin sensitivity. The 'phase 3' of individual teaching is an ongoing process of updating the patient's knowledge and practical skills.(ABSTRACT TRUNCATED AT 250 WORDS)     

Parameter identification of linear structural dynamic systems

The parameter estimations of linear multi-degree-of-freedom structural dynamic systems are carried out in time domain. Methods for estimating the system parameters and the modal parameters are presented. The equation of motion is transformed into the state space equation of the observable canonical form, and then into the auto-regressive and moving average model with auxiliary stochastic input (ARMAX) model to process the measurement data contaminated by the system noise as well as the output noise. The parameters of the ARMAX model are estimated by using the sequential prediction error method. Then, the parameters of equation of motion are recovered thereafter. In order to verify the accuracy of the estimation method, analytical simulation studies are performed for a model with two degrees of freedom on the basis of simulated data under various noise conditions. It is shown that the presented methods yield good estimates even under large noise conditions. The method is also applied to the identification of the modal parameters of a building model based on the experimental data.     

Estimates of ocean coherence time by an interferometric SAR

Abstract

The azimuthal resolution of the Synthetic Aperture Radar (SAR) when imaging the permanently moving ocean surface is determined by the coherence time of the imaged scene. The scene coherence time thus constitutes one of the major parameters in SAR imagery of the ocean. The present study shows how the direct estimate of this parameter under the actual experimental conditions can be performed using a two-antenna interferometric SAR. The present results arc in agreement with earlier estimates.     

Bayesian estimation based on trimmed samples from Pareto populations

Trimmed samples are widely employed in several areas of statistical practice, especially when some sample values at either or both extremes might have been contaminated. The problem of estimating the inequality and precision parameters of a Pareto distribution based on a trimmed sample and prior information is considered. From an inferential viewpoint, the problem of finding the highest posterior density (HPD) estimates of the Pareto parameters is discussed. The existence and uniqueness of the HPD estimates are established under mild conditions; explicit and accurate lower and upper bounds are also provided. Adopting a decision-theoretic perspective, several Bayesian estimators for standard loss functions are presented. In addition, two-sided and HPD credibility intervals for each Pareto parameter and joint HPD credibility regions for both parameters are derived, which have the corresponding frequentist confidence level in the noninformative case. Finally, an illustrative example concerning annual wage data is included.     

Parameter estimation for excavator arm using generalized Newton method

A robust, fast, and simple technique for the experimental identification of the link parameters (mass, inertia, and length) and friction coefficients of a full-scale excavator arm is presented. This new technique, based on the generalized Newton method (GNM), estimates unknown individual parameters of the excavator arm dynamic equations. The technique can be used when the number of equations is different from the number of estimated variables. Using experimental data from a full-scale field Combat Engineer Excavator (CEE), the values of link parameters and friction coefficients are successfully identified. The identified parameters are compared with known values, and shown to be in agreement. The method is compared with the least square method, and shows that the GNM is better in terms of prediction accuracy and robustness to noise. Further, the joint positions predicted by the analytical model using the identified parameters are validated against different experimental trajectories, showing very good agreement. The experimental data was obtained in collaboration with QinetiQ Ltd. (Hampshire, U.K.). The technique presented in this paper is general and can be applied to any manipulator.