David K. Melgaard

In vivo hyperspectral confocal fluorescence imaging to determine pigment localization and distribution in cyanobacterial cells

Hyperspectral confocal fluorescence imaging provides the opportunity to obtain individual fluorescence emission spectra in small (≈0.03-μm3) volumes. Using multivariate curve resolution, individual fluorescence components can be resolved, and their intensities can be calculated. Here we localize, in vivo, photosynthesis-related pigments (chlorophylls, phycobilins, and carotenoids) in wild-type and mutant cells of the cyanobacterium Synechocystis sp. PCC 6803. Cells were excited at 488 nm, exciting primarily phycobilins and carotenoids. Fluorescence from phycocyanin, allophycocyanin, allophycocyanin-B/terminal emitter, and chlorophyll a was resolved. Moreover, resonance-enhanced Raman signals and very weak fluorescence from carotenoids were observed. Phycobilin emission was most intense along the periphery of the cell whereas chlorophyll fluorescence was distributed more evenly throughout the cell, suggesting that fluorescing phycobilisomes are more prevalent along the outer thylakoids. Carotenoids were prevalent in the cell wall and also were present in thylakoids. Two chlorophyll fluorescence components were resolved: the short-wavelength component originates primarily from photosystem II and is most intense near the periphery of the cell; and the long-wavelength component that is attributed to photosystem I because it disappears in mutants lacking this photosystem is of higher relative intensity toward the inner rings of the thylakoids. Together, the results suggest compositional heterogeneity between thylakoid rings, with the inner thylakoids enriched in photosystem I. In cells depleted in chlorophyll, the amount of both chlorophyll emission components was decreased, confirming the accuracy of the spectral assignments. These results show that hyperspectral fluorescence imaging can provide unique information regarding pigment organization and localization in the cell.

New prediction-augmented classical least squares (PACLS) methods: Application to unmodeled interferents

A significant improvement to the classical least-squares (CLS) multivariate analysis method has been developed. The new method, called prediction-augmented classical least-squares (PACLS), removes the restriction for CLS that all interfering spectral species must be known and their concentrations included during the calibration. We demonstrate that PACLS can correct inadequate CLS models if spectral components left out of the calibration can be identified and if their “spectral shapes” can be derived and added during a PACLS prediction step. The new PACLS method is demonstrated for a system of dilute aqueous solutions containing urea, creatinine, and NaCl analytes with and without temperature variations. We demonstrate that if CLS calibrations are performed with only a single analytes concentrations, then there is little, if any, prediction ability. However, if pure-component spectra of analytes left out of the calibration are independently obtained and added during PACLS prediction, then the CLS prediction ability is corrected and predictions become comparable to that of a CLS calibration that contains all analyte concentrations. It is also demonstrated that constant-temperature CLS models can be used to predict variable-temperature data by employing the PACLS method augmented by the spectral shape of a temperature change of the water solvent. In this case, PACLS can also be used to predict sample temperature with a standard error of prediction of 0.07 °C even though the calibration data did not contain temperature variations. The PACLS method is also shown to be capable of modeling system drift to maintain a calibration in the presence of spectrometer drift.

New Classical Least-Squares/Partial Least-Squares Hybrid Algorithm for Spectral Analyses

A new classical least-squares/partial least-squares (CLS/PLS) hybrid algorithm has been developed that demonstrates the best features of both the CLS and PLS algorithms during the analysis of spectroscopic data. By adding our recently reported prediction-augmented classical least-squares (PACLS) to the hybrid algorithm, we have the additional benefit that known or empirically derived spectral shape information can be incorporated into the hybrid algorithm to correct for the presence of unmodeled sources of spectral variation. A detailed step-by-step description of the new hybrid algorithm in calibration and prediction is presented. The powerful capabilities of the new PACLS/PLS hybrid are demonstrated for near-infrared spectra of dilute aqueous solutions containing the analytes urea, creatinine, and NaCl. The PACLS/PLS method is demonstrated to correct the detrimental effects of unmodeled solution temperature changes and spectrometer drift in the multivariate spectral calibration models. Initially, PLS and PACLS/PLS predictions of analytes from variable-temperature solution spectra were made with models based upon spectra previously taken of the samples at constant temperature. The presence of unmodeled temperature variations and system drift caused the prediction errors from these models to be inflated by more than an order of magnitude relative to the cross-validated errors from the calibrations. PLS achieved improved predictions of the variable-temperature spectra by adding spectra of a few variable-temperature samples into the original calibration data followed by recalibration. PACLS/PLS predictions were corrected for temperature variations and system drift by adding spectral differences of the same subset of samples collected under constant- and variable-temperature conditions to the PACLS prediction portion of the hybrid algorithm during either calibration or prediction. Comparisons of the prediction ability of the hybrid algorithm relative to the PLS method using the same calibration and subset information demonstrated hybrid prediction improvements that were significant at least at the 0.01 level for all three analytes. The new hybrid algorithm has widespread uses, some of which are also discussed in the paper.

Hyperspectral Confocal Fluorescence Imaging: Exploring Alternative Multivariate Curve Resolution Approaches

Hyperspectral confocal fluorescence microscopy, when combined with multivariate curve resolution (MCR), provides a powerful new tool for improved quantitative imaging of multi-fluorophore samples. Generally, fully non-negatively constrained models are used in the constrained alternating least squares MCR analyses of hyperspectral images since real emission components are expected to have non-negative pure emission spectra and concentrations. However, in this paper, we demonstrate four separate cases in which partially constrained models are preferred over the fully constrained MCR models. These partially constrained MCR models can sometimes be preferred when system artifacts are present in the data or where small perturbations of the major emission components are present due to environmental effects or small geometric changes in the fluorescing species. Here we demonstrate that in the cases of hyperspectral images obtained from multicomponent spherical beads, autofluorescence from fixed lung epithelial cells, fluorescence of quantum dots in aqueous solutions, and images of mercurochrome-stained endosperm portions of a wild-type corn seed, these alternative, partially constrained MCR analyses provide improved interpretability of the MCR solutions. Often the system artifacts or environmental effects are more readily described as first and/or second derivatives of the main emission components in these alternative MCR solutions since they indicate spectral shifts and/or spectral broadening or narrowing of the emission bands, respectively. Thus, this paper serves to demonstrate the need to test alternative partially constrained models when analyzing hyperspectral images with MCR methods.

Concentration Residual Augmented Classical Least Squares (CRACLS): A Multivariate Calibration Method with Advantages over Partial Least Squares

A significant extension to the classical least-squares (CLS) algorithm called concentration residual augmented CLS (CRACLS) has been developed. Previously, unmodeled sources of spectral variation have rendered CLS models ineffective for most types of problems, but with the new CRACLS algorithm, CLS-type models can be applied to a significantly wider range of applications. This new quantitative multivariate spectral analysis algorithm iteratively augments the calibration matrix of reference concentrations with concentration residuals estimated during CLS prediction. Because these residuals represent linear combinations of the unmodeled spectrally active component concentrations, the effects of these components are removed from the calibration of the analytes of interest. This iterative process allows the development of a CLS-type calibration model comparable in prediction ability to implicit multivariate calibration methods such as partial least squares (PLS) even when unmodeled spectrally active components are present in the calibration sample spectra. In addition, CRACLS retains the improved qualitative spectral information of the CLS algorithm relative to PLS. More importantly, CRACLS provides a model compatible with the recently presented prediction-augmented CLS (PACLS) method. The CRACLS/PACLS combination generates an adaptable model that can achieve excellent prediction ability for samples of unknown composition that contain unmodeled sources of spectral variation. The CRACLS algorithm is demonstrated with both simulated and real data derived from a system of dilute aqueous solutions containing glucose, ethanol, and urea. The simulated data demonstrate the effectiveness of the new algorithm and help elucidate the principles behind the method. Using experimental data, we compare the prediction abilities of CRACLS and PLS during cross-validated calibration. In combination with PACLS, the CRACLS predictions are comparable to PLS for the prediction of the glucose, ethanol, and urea components for validation samples collected when significant instrument drift was present. However, the PLS predictions required recalibration using nonstandard cross-validated rotations while CRACLS/PACLS was rapidly updated during prediction without the need for time-consuming cross-validated recalibration. The CRACLS/PACLS algorithm provides a more general approach to removing the detrimental effects of unmodeled components.

New Hybrid Algorithm for Maintaining Multivariate Quantitative Calibrations of a Near-Infrared Spectrometer

Our newly developed prediction-augmented classical least-squares/partial least-squares (PACLS/PLS) hybrid algorithm can correct for the presence of unmodeled sources of spectral variation such as instrument drift by explicitly incorporating known or empirically derived information about the unmodeled spectral variation. We have tested the ability of the new hybrid algorithm to maintain a multivariate calibration in the presence of instrument drift using a near-infrared (NIR) spectrometer (7500–11 000 cm−1) to quantitate dilute aqueous solutions containing glucose, ethanol, and urea. The spectral variations required to update the multivariate models for both short- and long-term drift were obtained using a single representative midpoint sample whose spectrum was repeatedly measured during collection of calibration data and during collection of separate validation sample spectra on three subsequent days. The performance of the PACLS/PLS model for maintaining a calibration was compared to PLS with subset recalibration, a method that has previously been applied to maintenance and transfer of calibration. Without drift corrections, both PACLS/PLS and PLS had poor predictive ability on sample spectra collected on subsequent days. Unlike previous maintenance of calibration studies that corrected for long-term drift only, the PACLS/PLS and PLS models demonstrated the best predictive abilities when short-term drift was also corrected. The PACLS/PLS hybrid model outperformed PLS with subset recalibration for near real-time predictions when instrument drift was determined from the repeat samples closest in time to the measurement of the unknown. Near real-time standard errors of prediction (SEPs) for the hybrid model were comparable to the cross-validated SEPs obtained with the original calibration model.

New Hybrid Algorithm for Transferring Multivariate Quantitative Calibrations of Intra-vendor Near-Infrared Spectrometers

A new prediction-augmented classical least-squares/partial least-squares (PACLS/PLS) hybrid algorithm is ideally suited for use in transferring multivariate calibrations between spectrometers. Spectral variations such as instrument response differences can be explicitly incorporated into the algorithm through the use of subset sample spectra collected on both spectrometers. Two current calibration transfer methods, subset recalibration and piecewise direct standardization (PDS), also utilize subset sample spectra to facilitate transfer of calibration. The three methods were applied to the transfer of quantitative multivariate calibration models for near-infrared (NIR) data of organic samples containing chlorobenzene, heptane, and toluene between a primary and three secondary spectrometers that were all the same model, called intra-vendor transfer of calibration. The hybrid PACLS/PLS method outperformed subset recalibration and provided predictions equivalent to PDS with additive background correction on the two secondary spectrometers whose instrument drift appeared to be dominated by simple linear baseline variations. One of the secondary spectrometers had complex instrument drift that was captured by repeatedly measuring the spectrum of a single repeat sample. In calculating a transfer function to correct prediction spectra, PDS assumes no instrumental drift on the secondary spectrometer. Therefore, PDS was unable to directly accommodate both the subset samples and the use of a single repeat sample to transfer and maintain a calibration on that secondary instrument. In order to implement the transfer of calibration with PDS in the presence of complex instrument drift, recalibrated PLS models that included the repeat spectra from the secondary spectrometer were used to predict the spectra transformed by PDS. The importance of correcting for drift on the secondary spectrometer during calibration transfer was illustrated by the improvements in prediction for all three methods vs. using only the instrument response differences derived from the subset sample spectra. When the effects of instrument drift were complex on the secondary spectrometer, the PACLS/PLS hybrid algorithm outperformed both PDS and subset recalibration. Through the explicit incorporation of spectral variations, due to instrument response differences and drift on the secondary spectrometer, the PACLS/PLS algorithm was successful at intra-vendor transfer of calibrations between NIR spectrometers.

Multi-Window Classical Least Squares Multivariate Calibration Methods for Quantitative ICP-AES Analyses

The advent of inductively coupled plasma atomic emission spectrometers (ICP-AES) equipped with charge-coupled device (CCD) detector arrays allows the application of multivariate calibration methods to the quantitative analysis of spectral data. We have applied classical least-squares (CLS) methods to the analysis of a variety of samples containing up to 12 elements plus an internal standard. The elements included in the calibration models were Ag, Al, As, Au, Cd, Cr, Cu, Fe, Ni, Pb, Pd, and Se. By performing the CLS analysis separately in each of 46 spectral windows and by pooling the CLS concentration results for each element in all windows in a statistically efficient manner, we have been able to significantly improve the accuracy and precision of the ICP-AES analyses relative to the univariate and single-window multivariate methods supplied with the spectrometer. This new multi-window CLS (MWCLS) approach simplifies the analyses by providing a single concentration determination for each element from all spectral windows. Thus, the analyst does not have to perform the tedious task of reviewing the results from each window in an attempt to decide the correct value among discrepant analyses in one or more windows for each element. Furthermore, it is not necessary to construct a spectral correction model for each window prior to calibration and analysis. When one or more interfering elements were present, the new MWCLS method was able to reduce prediction errors compared to the single-window multivariate and univariate predictions. The MWCLS detection limits in the presence of multiple interferences are 15 ng/g (i.e., 15 ppb) or better for each element. In addition, errors with the new method are only slightly inflated when only a single target element is included in the calibration (i.e., knowledge of all other elements is excluded during calibration). The MWCLS method is found to be vastly superior to partial least-squares (PLS) in this case of limited numbers of calibration samples.

Effects of nonlinearities and uncorrelated or correlated errors in realistic simulated data on the prediction abilities of augmented classical least squares and partial least squares

Comparisons of prediction models from the new augmented classical least squares (ACLS) and partial least squares (PLS) multivariate spectral analysis methods were conducted using simulated data containing deviations from the idealized model. The simulated data were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions. Simulated uncorrelated concentration errors, uncorrelated and correlated spectral noise, and nonlinear spectral responses were included to evaluate the methods on situations representative of experimental data. The statistical significance of differences in prediction ability was evaluated using the Wilcoxon signed rank test. The prediction differences were found to be dependent on the type of noise added, the numbers of calibration samples, and the component being predicted. For analyses applied to simulated spectra with noise-free nonlinear response, PLS was shown to be statistically superior to ACLS for most of the cases. With added uncorrelated spectral noise, both methods performed comparably. Using 50 calibration samples with simulated correlated spectral noise, PLS showed an advantage in 3 out of 9 cases, but the advantage dropped to 1 out of 9 cases with 25 calibration samples. For cases with different noise distributions between calibration and validation, ACLS predictions were statistically better than PLS for two of the four components. Also, when experimentally derived correlated spectral error was added, ACLS gave better predictions that were statistically significant in 15 out of 24 cases simulated. On data sets with nonuniform noise, neither method was statistically better, although ACLS usually had smaller standard errors of prediction (SEPs). The varying results emphasize the need to use realistic simulations when making comparisons between various multivariate calibration methods. Even when the differences between the standard error of predictions were statistically significant, in most cases the differences in SEP were small. This study demonstrated that unlike CLS, ACLS is competitive with PLS in modeling nonlinearities in spectra without knowledge of all the component concentrations. This competitiveness is important when maintaining and transferring models for system drift, spectrometer differences, and unmodeled components, since ACLS models can be rapidly updated during prediction when used in conjunction with the prediction augmented classical least squares (PACLS) method, while PLS requires full recalibration.

A Nonlinear Reduced Order Model for Estimation and Control of Vacuum Arc Remelting of Metal Alloys

Vacuum arc remelting (VAR) is an industrial metallurgical process widely used throughout the specialty metals industry to cast large alloy ingots. The VAR process is carried out in a vacuum with the aim of melting a large consumable electrode (.4 m in diameter and 3000 kg in mass and larger) in such a way that that the resulting ingot has improved homogeneity. The VAR control problem consists of adjusting arc current to control electrode melt rate, which also depends on the electrode temperature distribution and adjusting electrode ram speed to control the arc gap between the electrode and the ingot. The process is governed by a 1 dimensional heat conduction partial differential equation with a moving boundary, which leads to an infinite dimensional, nonlinear system. In addition to the process nonlinearity, the inputs and all of the available measurements are corrupted with noise. In order to design a controller and a Kalman based estimator for this process, integral methods are used to derive a set of two coupled nonlinear ordinary differential equations in time, which capture the steady state and transient characteristics of melting in a VAR furnace. The model with the experimentally measured noise is then used to construct an estimator and a controller. The system can be described by two state variables that change in time: thermal boundary layer and melted length or alternatively electrode gap. The reduced order model compares favorably to an accurate finite difference model as well as melting data acquired for Ti-6Al-4V. It will be shown how this model can be used to obtain dynamic closed loop melt rate control while simultaneously controlling electrode gap. This controller and estimator were tested on a laboratory furnace at Timet.© 2005 ASME