Investigation of constrained regularization for the development of a robust and clinically accurate multivariate calibration procedure 18.086: Computational Science and Engineering II Spring 2008 Ishan Barman G.R. Harrison Spectroscopy Laboratory Massachusetts Institute of Technology1. INTRODUCTION Blood analytes provide valuable information for the diagnosis of many fatal diseases and abnormal health conditions. Development of painless and convenient methods for measurement of such analytes has received considerable attention. Glucose detection1, in particular, has been studied extensively over the last couple of decades as it has widespread implications in the control and management of diabetes. As diabetes has no known cure, tight control of glucose levels is critical for the prevention of such complications2. Given the necessity for regular monitoring of blood glucose, development of non-invasive glucose detection devices is essential to improve the quality of life of diabetic patients. Our laboratory has pioneered the development of a non-invasive glucose sensor based on the principles of NIR (near-infrared) Raman spectroscopy3,4. NIR Raman Spectroscopy combines the substantial penetration depth of NIR light with the excellent chemical specificity of Raman spectroscopy. Additionally, it enables the simultaneous determination of multiple blood analytes. The underlying principle of this technology is that the backscattered Raman photons, obtained by focusing a monochromatic source of light on biological tissue, have characteristic signatures of the analytes present in the tissue. The analytes of interest could be cholesterol, fats, proteins and glucose among a host of others. NIR Raman spectroscopy thus provides an excellent tool to meet the challenges involved in not only monitoring glucose levels but also diagnosing various pathophysiological conditions, such as cancer and atherosclerotic plaque. A number of major technical challenges, however, impede the development of a viable NIR Raman spectroscopic glucose sensor. Significant among these is the lack of robust and accurate information extraction algorithms, which can be applied to the spectra acquired in vivo. The poor signal to noise ratio of the Raman features makes a difficult task even more so. Further more, while the ability of Raman spectroscopy to detect multiple analytes simultaneously is a tremendous advantage, the extraction of analytical information about each of the constituents is not trivial – as in practice, most of these analytes tend to give overlapping features which do not readily lend themselves to quantitative predictions. In order to determine the concentration of the various analytes in a complex chemical system, multivariate calibration techniques are usually employed. Multivariate calibration algorithms, which can be utilized in a wide range of possible scenarios in terms of knowledge of the system under consideration, take the full-range spectrum into account5. This is critical as the complex spectra that are acquired in vivo cannot provide useful information if only a limited number of wavelengths are selected for analysis. The existing set of calibration algorithms can be broadly classified into explicit and implicit schemes. The explicit calibration procedures provide highly accurate models, but require complete knowledge of the constituents of the system and their corresponding (Raman) spectra. This limitation renders it of little value in most real life biomedical applications, where delineating the system constituents is a major task in itself. Implicit calibration, on the other hand, does not require knowledge of the constituent spectra, and can be used in applications where concentration information about the analyte of interest is known (or can be determined) in a set of reference samples. These calibration methods, however, are unable to distinguish between legitimate correlations between spectra and concentrations and spurious correlations,such as that obtained by system drift and high degree of (unrelated) covariance between constituents. Nevertheless, these techniques have gained widespread acceptability and function as the gold standard of the day. To alleviate the problems associated with the implicit calibration techniques, our laboratory has recently developed two hybrid calibration schemes, namely hybrid linear analysis (HLA) and constrained regularization (CR)6,7. CR, which provides more flexibility in the incorporation of the prior information than HLA, has been shown to significantly outperform the implicit calibration techniques in certain studies, where a reasonably high degree of correlation between at least two constituents of the samples is intentionally maintained (called correlated samples herein). In this study, our aim is to investigate the applicability of CR in more general situations, where sample constituents are uncorrelated (termed as uncorrelated samples). This would more closely mimic the prevalent situation in any glucose clamping or point of care clinical validation study. In this context, the concept of confidence maximization has been introduced. Confidence maximization is defined here as the weighted selection of samples and wavelengths in the calibration procedure, where larger weights are assigned to those samples and wavelengths that have greater probability of providing reliable and accurate constituent-specific information. In this article, we review the basic principles of the various multivariate calibration schemes that are pertinent to the introduction of the constrained regularization method. The theory of CR is then extended to include the formalism of confidence maximization. Next, an experimental study is presented to investigate the relative advantages in the application of CR over existing implicit methods for uncorrelated samples. Finally, we present results showing the substantial reduction in the prediction error that can be obtained by incorporating confidence maximization principles into the current CR formalism, especially for uncorrelated samples. 2. THEORY Establishment of relationships between measurements made on a system and the underlying state of the system is a key component of any experimental science. In chemistry, this idea has developed into a whole field of study, known as chemometrics. Chemometric analysis and interpretation of instrumental data utilizes well-established