Nonlinear curve fitting for bioelectrical impedance data analysis: a minimum ellipsoid volume method

Bioelectrical impedance spectroscopy has become a widely used method with various applications in physiological and clinical investigations. Its measurement results are often analysed using the Cole-Cole model in an attempt to relate its parameters to structural or physiological characteristics of the studied object. The model parameter values are usually assessed by nonlinear curve fitting based on the least mean square method. A new approach is proposed, leading to better accuracy. It is based on the notion that the difference between measured and model parameter values is randomly distributed with zero mean. The values of the unknown parameters are then deduced by minimizing the covariance matrix determinant. This method can be considered as a minimization of the volume of an ellipsoid, or ajoint minimization of two regressions having the same argument and common parameters.