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Biomedical Signal Processing and Control
journal homepage: www.elsevier.com/locate/bspc
A NARX modeling-based approach for evaluation of insulin sensitivity
S. Ghosh 1,*, S. Maka
Department of Electrical Engineering, IIT Kharagpur, Kharagpur, India
A R T I C L E I N F O
A B S T R AC T
Article history: Received 2 March 2008 Received in revised form 12 August 2008 Accepted 30 August 2008 Available online 16 October 2008 Keywords: IVGTT Autoregressive modeling Structure identiﬁcation Simulation reduction ratio Insulin sensitivity Minimal model
Evaluation of insulin sensitivity is of prime importance in the clinical investigation of glucose related diseases. This paperdeals with a novel model-based technique for the evaluation of an index for insulin sensitivity. A set of nonlinear autoregressive models are identiﬁed from the clinical test data of normal subjects. The two-stage identiﬁcation procedure involves proper structure selection for approximating the input–output data followed by estimating the parameters of the polynomial model. The models obtained areanalyzed to derive an index for insulin sensitivity by determining the effect of insulin on glucose utilization. A median bootstraped correlation (sampling with replacement) of 0.97 with 90% conﬁdence interval of [0.92 0.98], is obtained between the indexes of the proposed model and the widely used minimal model. The proposed model is able to achieve a good ﬁtting performance on the validationdataset. The results also suggest that for representing the dynamics of insulin action on glucose disposal, the proposed model overcomes some of the well known limitations of the minimal model, and thus gives a better representation of insulin sensitivity. ß 2008 Elsevier Ltd. All rights reserved.
1. Introduction Mathematical models relating the physiological interactions involved in blood glucosemetabolism has been developed by several researchers [1–8] since the last four decades. The models are mainly developed using the data of two easily accessible physiological variables: plasma glucose and insulin concentration. The regulatory mechanism postulated by the models accounts for the rise in glucose concentration by increasing the pancreatic insulin secretion, which enhances glucoseuptake and inhibits hepatic glucose production. Blood glucose metabolism-based models are able to quantify speciﬁc metabolic functions from the observed time course of glucose insulin kinetics and at the same time allow quantitive estimation of physiologically signiﬁcant parameters. Besides the physiological models some empirical models of blood glucose metabolism based only on the input–output timeseries data has also been reported. These include the models based on autoregression , volterra series  and neural networks . For physiological systems empirical models are useful when only limited prior information is available relative to the complexity of the system. Empirical models do not
* Corresponding author. E-mail addresses: firstname.lastname@example.org (S. Ghosh),email@example.com (S. Maka). 1 On study leave from BIT Mesra, Ranchi, India. 1746-8094/$ – see front matter ß 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2008.08.002
use any prior physiological information and are only compatible with the input–output data. Even though the parameters of the empirical models do not have any physiological signiﬁcance, but because of their good predictioncapability the development of these models are relevant to model predictive control (MPC) of blood glucose during diabetes mellitus and providing alerts for hypo/hyperglycemia conditions. One of the prime application of the physiological models has been on the quantiﬁcation of insulin sensitivity, which is the ability of insulin to increase glucose uptake by insulin dependent tissues and inhibit...