Weighted Linear Regression Improves Accuracy of Quantitative Elemental Bioimaging by Means of LA-ICP-MS

Abstract

The application of ordinary least squares (OLS) linear regression is widely used in order to approximate linear external calibration data. However, the assumption of homoscedasticity is often not considered as a requirement for correct data approximation, which can result in a poor regression fit that is often more prominent in the lower concentration range. Heteroscedasticity in inductively coupled plasma–mass spectrometry (ICP-MS) data has been discussed in literature as an intrinsic problem and was found to be addressed better by the use of weighted least squares (WLS) regression in multiple studies. In this study, the effects of OLS and WLS linear regression models have been investigated for quantitative imaging experiments by means of laser ablation (LA)–ICP-MS using matrix-matched standards. The calibration data produced by this technique was found to be heteroscedastic in all 60 analyzed datasets, which yielded poor regression fits for OLS linear regression. In comparison to conventional ICP-MS analysis, the resulting negative effects were found to become even more visible in imaging LA-ICP-MS due to an inaccurate estimation of the regression line’s intercept. Also, the calculation of average concentrations in selected regions of interest (ROIs) yields incorrect quantification results at the lower end of the calibration range. The application of WLS linear regression resulted in an improved goodness of fit (GOF), although the weighting factor should be selected carefully. Besides the reciprocal of the variance of each calibration standard (1/si 2 ) , more empirical weighting factors that have been discussed in the literature were also evaluated regarding the GOF.

Multiparametric MRI enables for differentiation of different degrees of malignancy in two murine models of breast cancer

“…The laser ablation system was connected via Tygon tubing directly to the 7700x ICP-MS (Agilent Technologies, Santa Clara, CA, U.S.A.). For external calibration, ten lines of each standard were ablated, and the averaged intensities of the validated element concentrations were analyzed with a weighted linear regression ( 20 ). Ablation of tumor slices was performed by a line-by-line scan.…”

LA-ICP-MS and Immunohistochemical Staining with Lanthanide-Labeled Antibodies to Study the Uptake of CeO2 Nanoparticles by Macrophages in Tissue Sections

“…To calculate the standard deviation even for low concentrations, a weighted linear regression (factor: 1/x 2 ) was used ranging from 0−10,000 μg• g −1 . 40 The LOQ was calculated according to the 10σ-criterion and even for the high-resolution analysis 0.08 μg•g −1 .…”

“…Based on these results, a high-resolution LA-ICP-MS analysis with a spot size of 4 μm was then conducted of a consecutive section. To calculate the standard deviation even for low concentrations, a weighted linear regression (factor: 1/ x 2 ) was used ranging from 0–10,000 μg·g –1 . The LOQ was calculated according to the 10σ-criterion and even for the high-resolution analysis 0.08 μg·g –1 .…”

Time resolved trace element calibration strategies for LA-ICP-MS

“…19 Additional methods can be employed by adding to the DRS script. For example, Funke et al 20 note that, due to heteroskedacity § in tting a calibration curve to LA-ICP-MS results, a WLS approach can provide additional accuracy especially if a custom weighting function is used. Although the latter is not currently implemented, it could be added by editing the provided script.…”