Comparing two fitting algorithms for determining the Cole-Cole parameters in blood glucose problems

Diabetes is a metabolic disease that affects millions of people around the world. Non-invasive electromagnetic techniques for continuous glucose monitoring (CGM) can greatly improve the lives of patients with diabetes and, for this reason, considerable progress has been made in recent years in the development of microwave sensors. In this framework, we face the problem of fitting the dielectric spectrum of glucose/water solutions in order to estimate the parameters of Debye or Cole-Cole models. Such models provide an efficient and accurate representation of biological tissues in the whole considered frequency band and reduce the complexity of the experimental data to a few parameters. Extracting a "synthetic view" of the dielectric properties of the tissues is essential to analyze the models and possibly to extract more information, in addition to the resonance peak or phase shift, on the glucose concentration. To this end, two different algorithms are used, namely the Levenberg-Marquardt and the variable projection algorithms, which are compared to address the underlying nonlinear problem by fitting the Cole-Cole model. Synthetic data of single-pole models, present in the literature, are used to evaluate the performances obtainable by these methods. In particular, the Monte Carlo analysis is used to evaluate how sensitive the two methods are with respect to the starting points of the parameters and how accurately the parameters can be estimated.