Quantification of Albumin and γ-Globulin Concentrations in an Electrolyte Solution by Multivariate-Regressive...

Albumin and γ-globulin concentrations in an electrolyte solution have been quantified by a multivariate-regressive Gaussian admittance relaxation times distribution (mgARTD). The mgARTD is built based on the training data consisting of the impedance spectroscopy system measurement result of protein mixture solutions with a known concentration of albumin, γ-globulin, and sodium electrolyte to perform concentration quantification on a prospective protein mixture solution with an unknown concentration. The mgARTD consists of three steps: (1) Prediction step of the peak matrix P* by Gaussian ARTD (gARTD) with the Gaussian process and peak detection algorithm, (2) Training step of the approximated coefficient matrix à based on the multivariate-regressive formula P* = Ac + φ (A: multivariate-regression coefficient matrix, φ: error matrix, and c: known concentration matrix of the training data set), and (3) Quantification step of the approximated concentration c̃ based on the Gauss-Newton algorithm from the predicted $\check{P^{*}}$ of the quantification data and the approximated Ã. In the experiments, first, à is approximated on the predicted P* and the known c under the 27 cases of protein and electrolyte concentrations (albumin: 0.800-2.400 g/dL, γ-globulin: 0.400-1.200 g/dL, and sodium electrolyte: 0.700-0.750 g/dL). Next, c̃ is determined by à and quantification data $\check{P^{*}}$ under an unknown albumin, γ-globulin, and sodium electrolyte concentration. The effect of albumin and γ-globulin on ARTD is observed in $\widehat{{\tau }_1^{*}}$ > 0.05 ms for counterion effects and in 10 μs > $\widehat{{\tau }_2^{*}}$ > 1 μs for protein reorientations. The gARTD γ* function achieves a transform fitting error of 10.90% on average, which is 12.12% lower than that of ARTD and minimizes the quantification error. The absolute percentage quantification error of c̃ by mgARTD is 9.90%, 9.12%, and 1.70% for albumin, globulin, and sodium electrolyte, respectively, which is significantly lower than 25.56%, 20.90%, and 25.71% for albumin, globulin, and sodium electrolyte by mARTD.