Parameter set uniqueness and confidence limits in model identification of insulin transport models from simulation data.

Background: The use of patient models describing the dynamics of glucose, insulin, and possibly other metabolic species associated with glucose regulation allows diabetes researchers to gain insights regarding novel therapies via simulation. However, such models are only useful when model parameters are effectively estimated with patient data.

Methods: The use of least squares to effectively estimate model parameters from simulation data was investigated by observing factors that influence the accuracy of estimates for the model parameters from a data set generated using a model with known parameters. An intravenous insulin pharmacokinetic model was used to generate the insulin response of a patient with type 1 diabetes mellitus to a series of step changes in the insulin infusion rate from an external insulin pump. The effects of using user-defined gradient and Hessian calculations on both parameter estimations and the 95% confidence limits of the estimated parameter sets were investigated.

Results: Estimations performed by either solver without user-supplied quantities were highly dependent on the initial guess of the parameter set, with relative confidence limits greater than +/-100%. The use of user-defined quantities allowed the one-compartment model parameters to be effectively estimated. While the two-compartment model parameter estimation still depended on the initial parameter set specification, confidence limits were decreased, and all fits to simulation data were very good.

Conclusions: The use of user-defined gradients and Hessian matrices results in more accurate parameter estimations for insulin transport models. Improved estimation could result in more accurate simulations for use in glucose control system design.