Anal. Chem. 1999, 71, 343R-350R
Infrared Spectroscopy Lily M. Ng* and Reiko Simmons
Chemistry Department, Cleveland State University, Cleveland, Ohio 44115 Infrared (IR) spectroscopy measures the absorption of infrared radiation by chemical bonds in a material. Chemical structural fragments of molecules, known as functional groups, tend to absorb IR radiation in the same frequency range regardless of the structure of the rest of the molecule that the functional group is in. This correlation between the structure of a molecule and the frequencies at which it absorbs IR radiation allows the structure of unknown molecules to be identified and structural or chemical changes of the molecule to be followed. The clinical applications of IR spectroscopy have been previously reviewed in 1996, covering significant applications of the methodology toward clinical diagnosis and noninvasive, in vivo monitoring from October 1994 to October 1996 (H1). This review covers the Chemical Abstracts period from October 1996 to October 1998. The organization of this contribution is slightly different from that of the previous biennal review. This article will briefly discuss recent advances in the application of IR spectroscopy in diagnostic analyses, laboratory analyses of pathological samples, and noninvasive in vivo monitoring, and examples of each will be presented. Emphasis will be placed on recent advancement of IR spectroscopy employed in the understanding of the process of diseases. Primarily the new technique of IR microspectroscopy will be covered in detail. In addition, basic theory and related data analysis techniques essential to the analysis of multicomponents in biofluids and solid biosamples and essential to the use of IR microspectroscopy in the detection of disease states will also be discussed in detail. REVIEWS The application of IR spectroscopy to clinical and biomedical analyses continues to increase throughout this review period. There has been a number of representative reviews and books published (H2-H11). Different infrared measurement techniques in the clinical analysis of biofluids were reviewed by Wang et al. (H3). The authors presented the spectra of physiological samples measured as liquids and thin films using transmission, attenuated total reflection, photoacoustic, and diffuse reflectance IR spectroscopy. They described the advantages and limitations of each of these techniques and discussed the development of routine analysis methods for biofluids. Three books have been published on spectroscopic methods for studies of biomolecules and specifically for IR methods including IR microscopy (H2, H4, H6). Jackson et al. reviewed IR spectroscopy as a new frontier in medicine (H7). They included 53 references on IR methodologies which comprise both instrumental (imaging and spatially localized IR spectroscopy) and interpretational procedures aimed at optimizing the measurements and their conversion to biodiagnostic information. A review with 15 references presents the great power of FT-IR spectroscopy in the field of medicinal biology (H8). 10.1021/a1999908r CCC: $18.00 Published on Web 05/20/1999
© 1999 American Chemical Society
Rintoul et al. demonstrated in their review article the versatility of modern FT-IR spectrometry by describing the range of some of the techniques available (H9). Examples drawn from biomedical research are included. A review of time-resolved infrared spectroscopy of biomolecules was written by Georg et al. (H10). The use of IR spectroscopy in the study of membrane lipids was discussed by Arrondo and Goni (H11). Specific topics discussed include the following: phospholipid band assignment, physical properties of membrane lipids, molecular order of membrane lipids, interactions of lipids with other membrane components, including other lipids and proteins, and the use of IR spectroscopy to study membrane lipids in living cells. CLINICAL APPLICATIONS The application of this analytical tool to clinical studies and diagnosis has generated a lot of enthusiasm as well as speculations (H8-H12) Recently, IR pathology is becoming increasingly important. Since diseases are manifested by changes in the composition of body fluids and tissues, these changes can be elucidated by the chemical information contained in their IR spectra. Diagnostic applications of IR provide the physicians an objective aid in the identification of the disease state or for staging the disease. This can be achieved with a pattern recognition approach. Quantitative analysis provides clinically relevant parameters in body fluids which may be used to indicate the metabolic status of the patient. The following applications show that IR spectroscopy has great promise as an accurate and rapid, multicomponent analytical technique in clinical chemistry. Diagnostic Application. IR spectroscopy has been increasingly applied to the diagnosis of diseases. The initial development is for convenient ways for routine screening and fast diagnosis, e.g., 13C-labeled urea breath test for screening for Helicobacter pylori infection; diagnosis of liver disease by the detection of 13CO2 in exhaled air. More recent developments have involved the combination of visible microscopy and IR spectroscopy in the identification of cancer cells and the elucidation of a possible mechanism of cell canceration and the progression of cancer to the metastatic state. Some examples of diagnostic applications are given in Table 13 (H13-H28). Laboratory Analyses of Pathological Samples. FT-IR spectroscopy has been used for fast multicomponent analyses of human blood and other pathological samples. Improvements in analysis are obtained by the adoption of multivariate calibration techniques as described below. For routine blood serum analysis, it is possible to use a partial least-squares algorithm to calculate the concentrations of cholesterol, triglycerides, glucose, total protein, lipid, urea, and uric acid. In addition to blood serum, other pathological samples have also been analyzed by IR spectroscopy. Fecal fat and fecal carbohydrates can be studied by near-IR Analytical Chemistry, Vol. 71, No. 12, June 15, 1999 343R
Table 13. Examples of Diagnostic Application of IR Spectroscopy diseases/conditions
analytes
breast cancer breast cancer astrocytomas cervical lesions/cancer
DNA tissues protein tissues, cells
lymphoid tumors drug resistance biocatalytic activity metabolite overproduction skin cancer single cell screening bone diseases
techniques
refs
RNA/DNA cells model systems model systems
microspectroscopy FEW-FT-IR microspectroscopy high-pressure FT-IR microspectroscopy FT-IR microspectroscopy FT-IR DRASTIC DRASTIC
H13, H14 H15, H25 H16 H26 H22 H24 H18, H27 H19 H20 H20
tissues DNA, proteins, lipids bone samples
fiber-optic ATR sychrotron microspectrometry microspectroscopy
H21 H23 H28
Table 14. Examples of Pathological Samples Analyzed by IR Spectroscopy samples
analytes
gallstones
cholesterol, bilirubinate salt, elements fecal fat fat contents calcified tissues minerals human adipose trans-fatty acids tissue synovial fluid synovial fluid serum, blood multicomponents amniotic fluid lipase serum biomembrane tissues urine iliac crest biopsies cortical bones blood hair
techniques microspectroscopy near-IR photoacoustic IR ATR
refs H29, H30, H46, H48 H31, H32 H33 H34
near-IR near-IR
amniotic fluid lipase multicomponents vesicles Hb, HbO2, Cytaa3, Icg urease mineral contents
H35 H35, H43, H44 near-IR H35 ATR H36 laser excitation IR H37 surface-enhanced IR H38 near-IR H39 FT-IR H40 microspectroscopy H41
minerals and matrix glucose drugs
microspectroscopy FEW-FT-IR microscopy
H42 H45 H47
reflectance analysis. IR analysis of stool samples is fast and does not require unpopular sample handling. Results indicate that nearIR spectroscopy may be a new, reliable, and accurate test in the diagnosis of carbohydrates and fat malabsorption. Other samples such as gallstones, urinary stones, tissues, bones, and urine samples have also been analyzed. Selective examples of IR pathological analyses are listed in Table 14 (H29-H48). Noninvasive in Vivo Monitoring. In vitro monitoring is inherently invasive, and the results are often delayed 1 h or more when the analyses are performed in the central laboratory. The delay may be greatly reduced if the analyses are performed near the patient. In vivo monitoring may be noninvasive and may provide continuous real-time data, but the accuracy sometimes does not match that of in vitro measurements. In vivo monitoring is best applied in the detection of trends of change, and it is used for quantities that change rapidly and unpredictably and where a suitable therapeutic action is available. Near-IR spectroscopy is normally used for monitoring. Examples of noninvasive in vivo monitoring include oxy- and deoxyhemoglobin in the brain, blood glucose, bilirubin, albium, urea, cholesterol, tissue oxygenation, cerebral circulation and oxygen metabolism during surgery, cerebral blood volume, and cytochrome oxidase. Examples of these are listed in Table 15 (H49-H77). Monitoring of Drug/Medicine Metabolism. IR spectroscopy is used routinely for the identification and structural determination 344R
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Table 15. Examples of Noninvasive in Vivo Monitoring by IR Spectroscopy samples
analytes
refs
blood (through skin) glucose
H49, H50, H52, H54, H55, H56, H57, H72 tissue, muscle oxygen H51, H53, H59, H60, H62, H67, H68, H69, H74 blood (through skin) hemoglobin H53, H55, H56, H57, H61, H63, H65, H75 tissue, muscle hemoglobin, oxy-Hb H55, H56, H57, H61, H66, H69, H75 brain/cerebral Hb, oxy-Hb H63, H68, H71, H63 blood (through skin) urea, cholesterol H57, H65 blood (through skin) albumin, proteins H57, H58, H65 muscle phosphocreatine H62 muscle glycolytic metabolites H64 mammalian fluids nitric oxide H70 tissue, blood pH H76, H77
of new pharmaceutical compounds. A new application of IR spectroscopy in clinical chemistry is the monitoring of drug/ medicine metabolism in the body. It can be used to determine the concentration of drugs and the metabolites in body fluids or body parts, e.g., in hair. A breath test has also been used with an isotopically labeled drug to determine the concentration of a metabolite of the drug. The concentration of the metabolite is then used to determined the rate of metabolism of the drug. The effects of drugs in vitro can also be monitored by the changes in cell viability after treatment with drug using FT-IR microspectroscopy. Ex vivo drug response, sensitivity or resistance to drugs, can be predicted by the IR spectra of the diseased cells before and after treatment of the patients with the drugs. Examples are shown in Table 16 (H78-H88). IR MICROSPECTROSCOPY Infrared microspectroscopy is the coupling of optical microscopy and infrared spectroscopy. IR microspectroscopy is attractive because it combines IR spectroscopy’s ability to identify subtle differences in the chemical components and optical microscopy’s capability to spatially resolve the location of sample features. It allows the visual and infrared examination of different parts of the sample on the microscopic scale. This technique is particularly attractive because it is highly sensitive. The infrared microscope can be used in four ways: visual transmission, visual reflection, infrared transmission, and infrared reflection. Detailed descriptions of microscope designs can be found in the literature (H5, H6, H13, H89-H91). In infrared microscopy, it is imperative that the sample and background spectra be run using the same settings. This is as important as using the same number of scans and the same resolution for these spectra. The sample spectrum is usually taken before the background spectrum and the ratio of two spectra is taken at a later time to obtain the absorbance or transmittance spectrum. Infrared spectra of microscopic samples can also be obtained in reflectance. The sample is typically mounted on a gold mirror and the infrared beam is reflected off the sample. The background spectrum is obtained by reflecting the infrared beam off a clean portion of the gold mirror. Infrared microspectroscopy has great potential as a biochemical and biomedical probe. In contrast to conventional histological techniques, IR spectral images are derived from the intrinsic vibrational properties of the biological components. The IR spectra reflect changes in biochemical and biophysical properties resulting
Table 16. Examples of Monitoring of Drug/Medicine Metabolism by IR Spectroscopy drug/medicine various medicaments drug administered by transdermal delivery drug detectable in hair isotopically labeled drug tetracycline bryostatin 1, 2-chlorodeoxyadenosine indomethacin, ibuprofen propofol (an anesthetic drug) adamantyl maleimide
methodology noninvasive IR detection of the medicine, metabolites, or markers (patent) noninvasive quantification by IR of diffusing species (e.g., salicylic acid) through artificial neural network (research model) probe of longitudinal sections of hair along growth line for time measurement; probe of cross sections to review hydrophobic/hydrophilc characteristics of drug by IR microspectroscopy (clinical) detection of isotopically labeled carbon dioxide or other metabolites in the breath for rate of metabolism (clinical) tracking of rate of release from local drug delivery sytem consisting of PLGA films (research) detection of cell membrane changes as basis of predicting ex vivo drug response (sensitivity/resistance) (preclinical) detection of effects on cerebral perfusion and oxygenation of iv ibuprofen and indomethacin treatment in preterm infants by noninvasive near-IR (clinical) study of magnesium-propofol interaction in vitro as related to fluctuations of Mg in serum after clinical administration of propofol (research) study of conformational changes in gastric carcinoma cell membrane protein after treatment by microspectrosopy (research)
from disease or toxic injuries. Using IR microspectroscopy, these intrinsic changes across a sample can be visualized. Kidney stones, arteries, and individual cells have been studied using this technique. One of the most exciting development in the field is the discovery that healthy and cancerous cells have different infrared spectra (H5, H7, H13, H89, H92). Chemically induced DNA damages that prompt the progression of cancers to the metastatic state can also be detected (H13). Mapping. To define the area of the sample to be analyzed, physical apertures are placed in the beam path such that radiation is sampled only from a well-specified region of the sample. To acquire spatially resolved spectral images using this technique, a sampling area is first defined by the apertures. Spectral data are then obtained from this region, the sample is moved so that the apertures are focused on an adjacent portion of the sample, and spectral data are again obtained. The whole process is repeated until the desired sampling region is mapped. A typical spectrum with 4-cm-1 resolution in the 700-4000-cm-1 range can be obtained in ∼30 s. The smallest regions that can be probed are on the order of 15 µm. The major drawbacks of using mapping for the collection of spatially resolved images are the long collection times and the limited spatial resolution. Imaging. FT-IR spectral imaging can be accomplished by a new instrument that incorporates a step-scan Fourier transform interferometer, a microscope, and a focal plane array. This instrument simultaneously obtains high-resolution IR spectra for each pixel of a two-dimensional imaging array. This new technique has been applied to the identification of leaking silicone from breast implants, metastatic cells and tissues, and neurotoxicity (H2, H5). It shows great promise for diagnosis of pathologies resulting from disease and toxic insult. DATA ANALYSIS TECHNIQUES The raw data obtained from an FT-IR spectrometer are often put through spectral manipulations. The main goal of such spectral manipulations is to extract more information, which can supply possible hints for further interpretations. Understanding and working with the IR data is crucial because the raw measurements often appear simple yet contain much qualitative and quantitative information. As the researchers struggle to glean insights into the studies of bioanalytical and clinical samples with FT-IR, various approaches are developed and utilized. Currently, there are many software which will allow quick access to these methods. Follow-
refs H78 H79 H80 H81 H82 H83-H85 H86 H87 H88
ing are a few, generally well-accepted methods especially applicable to clinical chemistry research. Spectral Subtraction. The principle behind spectral subtraction is easy to understand. A spectrum of a mixture such as a protein being studied in solution is called a “sample” spectrum. On the other hand, a “reference” spectrum is one component of the mixture such as water for the above example. A set of subtractions can be performed, point by point, to subtract away the absorbance values of the reference from the sample spectra to obtain the difference. When performed following certain stipulations, the results can show peaks attributable to the nonreference material that were previously hidden. A closer examination of the above principle reveals that the validity of Beer’s law must hold for both spectra in question. Specifically, the units of the spectra must be linearly proportional to concentration. Usually, the concentration of the sample and the reference will not be the same. If the linearity relationship holds for the two spectra, however, a factor can be multiplied to the reference spectrum to resolve this problem. In their studies of the metal-DNA interaction, Tajmir-Riahi et al. utilized the difference spectra algorism: [(DNA solution + metal cation solution) - (DNA solution)] (H93). These authors mentioned the use of certain DNA bands as internal reference. They reasoned that the band at 893 cm-1 was useful because its absorbance is due to deoxyribose-phosphate vibrations and exhibited no change upon complexation of DNA with cation. In other words, this band will cancel out completely when subtraction is performed. The main data analysis method used by Rothschild and Marrero, in their studies of the light-activated membrane protein bacteriorhodopsin, was also difference spectrometry (H94). By performing the subtraction, they were successful in pinpointing the absorption changes due to the alterations in the protein. Bagley et al. also studied rhodopsin but took the FT-IR subtraction method a step further. They were successful in setting up an innovative experimental design whereby three different products of “photosequence”, rhodopsin, bathorhodopsin, and isorhodopsin, were compared. Due to the light absorption, rhodopsin is known to go through a sequence of changes, which triggers electrical conversion of the photoreceptor cell membrane. This conversion of electrical properties, in turn, results in the neural signal. By pairing the three products (bathorhodopsin/ rhodopsin, bathorhodopsin/isorhodopsin, isorhodopsin/rhodopsin) and calculating the difference spectra for each pair, researchAnalytical Chemistry, Vol. 71, No. 12, June 15, 1999
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ers were able to obtain information regarding “the proteinchromophore linkage, isomeric state, and opsin conformation” (H95). As these researchers were interested in the complex changes occurring with time, several scans representing certain time intervals were paired and subtracted from each other. Thus, the study was able to focus on the detailed differences occurring during the time scale of the experiment (H95). Advantages and some practical considerations regarding the use of attenuated totasl reflection (ATR) in the studies of whole blood and plasma are carefully outlined by Wang et al. (H3). They caution against achieving a single water subtraction factor when various thicknesses and concentrations of biofluids are studied. Water, blood and plasma can have different refractive indexes and penetration depths of the evanescent waves. The resulting spectra may show high variability in intensities. Therefore, it is especially important to be mindful of the conditions affecting the subtrahend in the clinical analysis of biofluids. Spectral Derivatives. Many of the articles and reviews regarding spectral derivatives mention the original study of the second-derivative spectra of proteins in 2H2O by Susi and Byler (H96). The second derivative of the original spectrum offers a direct way to identify the peak frequencies of characteristic components and thus permits much more detailed qualitative and, eventually, quantitative studies. An infrared spectrum is a mathematical funtion; therefore, one can calculate and determine the slope of such function by taking the derivative. Currently, most computer software will furnish several methods, such as “Point Difference”, “Savitsky-Golay”, etc., which will calculate several orders (i.e., first through ninth) of derivatives. The main purpose of obtaining the derivatives is not to obtain the value of the “slope” but to use the information contained in the resulting derivative spectrum. The second derivative is most useful because it contains three features corresponding to each peak in the original spectra. In particular, the bottom of the downward pointing feature pinpoints the exact wavenumber of the maximum absorbance of the peak. These wavenumbers then, can be used in turn to estimate the number of overlapping bands in the composite and to locate their possible peak positions. Further explanation of the use of the derivatives will be found in the following section regarding Deconvolution. Deconvolution. Deconvolution can be one of the most useful and powerful methods of interpreting the IR spectra. Biochemical analysis of protein secondary structure continues to be a popular topic of investigation, originating in the early 1980s. The amide I band is often studied in relation with the changes in the protein structure. It is generally known that the amide I band consists of a number of overlapping component bands. Many researchers worked to establish the correspondence between the protein structural changes and the changes in the IR band components. This approach leads to various attempts to resolve the large composite band into separate narrower bands for the purpose of identification. In 1981, Kauppinen et al. developed a computational method entitled, “a digital self-deconvolution method” (H97). It is known today as Fourier self-deconvolution (FSD) and is widely used as the most effective procedure of narrowing infrared bands (H98). Applications of deconvolution methodology provide the possibilities of detailed protein secondary structural analysis. The spectra resolved by FSD can be helpful in studying subtle spectral 346R
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changes brought about because of an external parameter. Once the correlation between resolved components in amide band areas and specific polypeptide structures is established, researchers can design novel approaches to observe structural changes. Using various experimental designs, parameters such as temperature, pressure, concentration, pH, and solvent can be varied and the resulting detailed structural changes can be observed. Although applicable to all types of protein, Surewicz and Mantsch point out the fact that the method is especially helpful in studies of membrane proteins in the hydrophobic environment of the lipid bilayer (H98). The infrared study of this particular species of protein tends not to be hampered by the problems encountered in X-ray diffraction or CD spectra (e.g., unavailability of quality crystals, distortions of CD spectra by large membrane fragments, etc.). A review by Surewicz and Mantsch includes a large section regarding the applications of resolution enhancement for the studies of protein secondary structure (H98). They listed studies of Ca2+ transport ATPase from sarcoplasmic reticulum, bacteriorhodopsin, myelin basic protein, β-lactoglobulin, methionine aporepressor from E. coli, and two peptide hormones. Investigations of protein structural changes using FSD frequently make comparisons of percentages of areas under the component bands with percentages of the conformational structures (R-, β-turns, etc.) referenced by other experimental techniques. An assumption is made above that the effective absorptivities of the observed bands are “very similar” for the corresponding, yet, different conformational structures (H98). According to Surewicz and Mantsch, studies showed good correlation “for about 20 proteins between the secondary structure estimates obtained from X-ray data and infrared analysis” (H96, H98). They concluded that although the general validity remains to be tested, the assumption appears to be reasonable. Neverthless, they warned against the use of these estimated percentages as absolute values of the structural contents. Jakobsen and Wasacz conducted an extensive study of infrared spectra and structure correlations of albumin and managed to assign a vibrational assignment for most of the observed bands (H99). Along with the band assignments, they studied the conformational changes upon and during adsorption. Deconvolution was the method they utilized for all spectra in their paper; however, they based their results on several approaches: past assignments, their own experimental justifications, Raman spectra, and a special software program. This software enabled the researchers to calculate “the percentage contribution of each amino acid to the intensity at any frequency”. The infrared spectra of the 20 amino acids that make up the primary sequence of a protein were used to come up with “a composite spectrum”. This composite spectrum was based on “the weight percentage of each amino acid present in the protein”. Multivariate Analysis. In bioanalytical and clinical studies, a researcher is rarely faced with the analysis of a single component. The complexity of biological systems demands multicomponent quantitative analysis. At the same time, the quantity of spectra taken in a typical near-IR or mid-IR experiment could easily number in the hundreds. When combined with the range of the wavelengths, the data points involved quickly become large. Yet, despite the potentially high information content of the FT-IR measurements, without a sound analysis technique, the qualitative
and quantitative information could remain buried. This is why bio/ clinical studies using FT-IR call for multivariate data analysis. In recent years, mathematical, statistical, database, and expert system techniques have come together to be known as chemometrics. Multivariate data analysis is a good example of chemometrics applied to the spectroscopic data. At the time it was published (1990), Davies stated that, “a considerable number of multivariate data analysis methods exist”, and new methods are constantly being developed (H100). An attempt will be made to summarize a few major categories with emphasis on the basic understanding and the practical information. The term “multivariate analysis” is often used for analysis dealing with multicomponent data. Most multivariate analysis applied to chemical data are based on the least-squares (LS) techniques (H101). At the same time, all multicomponent spectral analyses are based on the additivity of Beer’s law. The additivity of Beer’s law may be expressed in the following sequential steps:
(a) for a series of components at a single absorbance, A(ν) )
∑a (ν)lc i
i
(at the ith component of the mixture)
(b) for a range of absorbance (a spectrum) of a mixture, Aj )
∑a lc i
ji
(where A, a, and c are vectors)
(c) for a series of absorbance spectra with components of linearly independent concentrations, A ) ELC (where the equation is expressed in a matrix form) where A is the vector of absorbances, E is the matrix of absorptivities, L is the vector of path lengths, and C is the vector of concentrations. (All vectors and matrices are denoted in bold text.) This expression in the matrix form is important because various methods in multicomponent analysis begin with the above form. In fact, various quantitative analyses differ only in the ways in which they perform matrix algebra upon the data represented in the above format. The initial step for the multivariate analysis is the calibration step to obtain the standard spectra. The experimental design must provide for standards with known concentrations of the components of interest. Thus, the information regarding A, L, and C is provided by the standards and the values of E will be supplied by the calibration. After the calibration is performed, the concentrations of unknowns can be predicted by measuring the sample absorbances and entering the appropriate values into the calculations. Least-Squares Methods. Use of linear regression is a fundamental and classical approach. Two approaches involving the LS method will be summarized. (a) Classical Least-Squares (CLS) or K Matrix Method. In this approach, path length and absorptivity matrices are combined into a single matrix called K. Therefore, the basic equation is, K ) EL and A ) KC, with the absorbance expressed as a function of the concentration. Taking the K matrix, a matrix operation called “least-squares fit” is performed to produce, by definition, “the best available model of the data” (H2). When K is
determined, the unknown concentrations comprising the matrix C can be calculated through another matrix operation. The advantage of the K matrix method is the relatively straightforward mathematics involved. Also, if so desired, use of this method permits “an averaging effect” by use of many standards and wavenumbers in the calibration. There are two basic limitations: (i) its sensitivity to presence of impurities or unexpected components and (ii) its intolerance of interactions between the sample components. These limitations require, first, that the standards not have any impurities. Also, all components and their concentrations must be known prior to analysis. If impurities are present in the samples, since they must be included in K-matrix presentation, researchers must be fully aware of their existence. The researchers, in other words, must know the complete chemical composition prior to analysis. This can be a tall order in the case of a complex system such as bio/clinical samples. For these reasons, applications of the K matrix work best where the sample compositions are predictable and interactions between components are nonexistant. (b) Inverse Least-Squares (ILS) or P Matrix Method. The original matrix expression A ) ELC can be rewritten as, C ) PA, where P ) (EL)-1. In this format, the concentration is a function of absorbance. Therefore, even if the concentration of an impurity is not taken into account, the P-matrix can be obtained as long as there are as many absorbance measures as there are concentrations. Consequently, with P matrix operation, the same least-squares matrix manipulation can be performed successfully with only the concentrations of the known components. According to Griffiths et al., P matrix can be very timeconsuming (H102). One must ensure that there are as many absorbance measurements as components, and these absorbance measures must be sensitive to changes in concentration. Generally, this means preparing and running many standards. Yet, not every wavenumber in an entire spectrum can be selected to perform the analysis; therefore, it makes inefficient use of the data. However, in a practical situation, an accounting for every component in a sample is difficult. For this reason, the P matrix method is often chosen. Factor Analysis. The aim of the factor analysis approach is to develop a meaningful mathematical model of the chemical system and use it to predict the properties of test samples (H100). Its major strength is the ability to aid the analyst in isolating the desired information that may be hidden in relatively large amounts of data (H103). Factor analysis is a general technique which has been applied to a wide variety of problems. Apparently, Antoon et al. first applied the factor analysis approach to IR spectroscopy (H102). As a technique, in addition to “factor analysis”, the method employs some form of linear regression to reach the final analytical results. There are several factor analysis methods, and in addition, many variations have evolved. Two major types will be introduced: principal component regression (PCR) and partial least squares (PSL). Since these methods are intended for routine, rapid, and nondestructive determination of the chemical composition, they are especially suited for clinical analysis (H104). When these methods are employed using computer software, the analysis is performed on the entire spectrum with no special requirements for selections of peaks, baselines, etc. They may Analytical Chemistry, Vol. 71, No. 12, June 15, 1999
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be used when the spectral bands are overlapped or affected by baseline variations, spectral noise, purge variations, sample impurities, and nonlinear response. (a) Principal Component Regression. In PCR, prior to the application of the “regression” technique, the information content is distilled into a smaller number of principal components. Those principal components that correlate strongly with the calibration set of concentration values are used to develop the model system, while those with low correlations are dropped. Thus, the method can indicate the errors associated with the prediction and the validity of applying the model (H100). When the data from the standard spectra are entered, the program will compute the average of these spectra. Each standard spectrum, then, is compared to the average spectrum and a new spectrum called factor is calculated. The factor describes the difference between the standard and the average. The amount of the factor in each standard spectrum is called a score. Each score is multiplied by the factor, and the product is subtracted from each standard spectrum. The result of the subtraction is called a residual. The residuals in turn are used in the next iteration to calculate a new average spectrum, a new factor, and a new set of scores. This is how, each time, the iteration process will strip the spectral contribution of some components from the standard spectra. Using the method described above, the factor analysis accounts for the variability in the standard specta. It will be wise to keep in mind that the computer program does not know how many factors are needed to best describe the data. The iteration will continue until the user stops the process. In fact, several authors point to the determination of the optimum number of factors as the key to the use of factor analysis (H2, H100, H103, H105). Some experimentation and practice, as well as the use of “cross-validation” will be required for best results. (b) Partial Least Squares. According to McClure and Lehmann, the partial least-squares method was developed by Wold and co-workers (H103). PSL differs from PCR in that information contained in both the dependent and independent variables (absorbance and concentration) play a role in the development of the calibration model (H2, H100, H103). Davis also stated that PSL tends to show relevance toward chemical values, since the chemical data are used to find a pattern in the data that correlates with factors (H100). In their chapter describing the software, “Computerized Infrared Calculations on Materials” (CIRCOM), McClure and Lehmann give an example of a study of lipids. They analyzed IR spectra of 21 synthetic mixtures of 14 lipids found in serum (H103). They concluded that the method, which is an offshoot of PCR, made successful predictions for triglycerides, lecithin, sphingomyelin, free cholesterol, and esterified cholesterol. The results for fatty acids were usable for the differentiation of normal and potentially pathological. They did not feel their results were useful for other lipids included in the study. They remarked that the study was a beginning of “a more extensive investigation of multiple lipid analysis”. Closer analysis of this example may shed some light regarding the details of PCR method. Heise and Bittner studied blood substrates in human plasma using PSL (H106). The substrates they chose to study were total protein, glucose, total cholesterol, triglycerides, and urea. Nearinfrared, ATR spectroscopy was utilized. They employed a “crossvalidation” method to verify the calibration results. This article 348R
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with its many references gives a useful description of the development of a multicomponent assay. The study conducted by Malins et al. was the linkage of hydroxyl radical-induced DNA damage with the metastatic state of human breast cancers. The experimental design used the IR spectra in an innovative manner. A three-dimensional plot of principal components from factor analysis was constructed to help visualize the spectral relationship of the cancer and noncancer DNA groups (H13). The authors stated that, “future research may confirm that Principal Component Analysis (PCA) of FTIR spectra is a promising technique with high structural specificity for discriminating DNA phenotypes in cancer diagnosis and prediction”. In summary, with an aid of a good software, multivariate analysis can be a useful method in handling a large set of complex data. Smith states, “as long as a physical or chemical property of a sample causes the sample’s spectrum to change, the spectral changes and measurements of the property can be correlated” (H2). Furthermore, by simply obtaining their spectrum, these properties can be predicted for various experimental samples. Using the above-mentioned multicomponent analysis methods, one is able to obtain useful predictions from complex bio/clinical data. In general, then, use of IR spectra can save time and expense in terms of analysis as well as sample preparations. Lily M. Ng is an associate professor and the Associate Chair of the chemistry department at Cleveland State University. She received her B.A degree in environmental science from Governors State University (Illinois) in 1978 and Ph.D. degree in physical chemistry from University of Pittsburgh in 1985. She was a Postdoctoral Associate and a Research Assistant Professor at University of Pittsburgh from 1984 to 1987. Her current research interest is in the application of infrared spectroscopy to novel systems, and one of the current projects in her research group is the study of conformational changes of proteins and DNA under different chemical environments by infrared spectroscopy. Reiko Simmons is a doctoral candidate in the Department of Chemistry at Cleveland State University. She received her M.Ed. degree from Kent State University in 1970 and her M.S. degree in chemistry in 1999. Her research involves infrared spectroscopic studies of the degradation of myelin by chemical compounds.
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