Quantitative Biological Raman Spectroscopy

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12Quantitative Biological Raman SpectroscopyWei-Chuan Shih, Kate L. Bechtel, and Michael S. FeldGeorge R. Harrison Spectroscopy Laboratory Massachusetts Institute of TechnologyCambridge, MA ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Quantitative Considerations for Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . .Biological Considerations for Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . .Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Data Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .In Vitro and In Vivo Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Toward Prospective Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .366367370373376378383386392392393Raman spectroscopy is a powerful technique for identifying the molecular composition of materials. It can also be used to quantify the substances present. Recently,quantitative Raman spectroscopy has been used in biological tissue for disease diagnosis and, in blood, to measure concentrations of analytes such as glucose noninvasively. A characteristic feature of biological tissue is its high turbidity, due tothe interplay of scattering and absorption. In addition, the complexity of biologicaltissue results in significant spectral overlap. These factors make the quantificationof analyte concentrations difficult. Measurement accuracy can be improved if thesedifficulties can be overcome. This chapter discusses the application of quantitativeRaman spectroscopy to biological tissue. Section 12.1 provides an introduction toRaman spectroscopy. Section 12.2 reviews existing work relevant to quantitativeanalysis in biological media. Quantitative and biological aspects of Raman spectroscopy are discussed in sections 12.3 and 12.4. Section 12.5 discusses instrumentation, using the instrument developed in our laboratory as an example. Data preprocessing is discussed in section 12.6. In section 12.7 we review our glucose studiesin blood serum, whole blood and human subjects. Section 12.8 introduces two newtechniques, constrained regularization (CR) and intrinsic Raman spectroscopy (IRS),which are shown to significantly improve measurement accuracy. Additional consid-365

366Glucose optical sensing and impacterations are discussed in the context of future directions. Section 12.9 concludes thechapter.Key words: Raman spectroscopy, glucose sensing, turbidity, scattering, absorption,biological tissue, intrinsic Raman spectroscopy (IRS).12.1 Introduction12.1.1Introduction to Raman spectroscopyLight scattering is a well-known form of the light-matter interaction process. Scattering redirects light incident on an atom or molecule. Most of the scattered light hasthe same frequency as the incident light, and therefore there is no energy exchange.This process is called elastic scattering and, for scatterers small compared to thewavelength, it gives rise to Rayleigh scattering. A tiny amount of the scattered light,however, is shifted in frequency due to transfer of energy, most commonly vibrational energy, to or from the molecule. The excitation light can set the moleculeinto vibration at the molecular vibrational frequency, νV . This process, called Raman scattering, is an inelastic scattering process, as energy is exchanged between themolecule and the incident light.From a quantum-mechanical point of view, an incident photon of frequency νL ,wavelength (c0 /νL ), and energy hνL , with c0 the speed of light and h Planck’s constant, is instantaneously taken up by the molecule, forming a “virtual state” that isusually lower in energy than the electronic transitions of the molecule. A new photonis created and scattered from this virtual state. If the new photon is down-shifted infrequency, the process is called Stokes-Raman scattering [1]. The resulting photonwill have a reduced energy h(νL νV ). Similarly, a molecule can begin in an excitedvibrational state and proceed, via the virtual state, to the ground state. This generates an up-shifted “anti-Stokes” Raman scattered photon, with an increased energyh(νL νV ). The processes of Rayleigh, Stokes Raman, anti-Stokes Raman with unshifted, down-shifted, and up-shifted frequencies of the scattered light, respectively,are illustrated in Fig. 12.1.Raman scattering, discovered by Raman and Krishnan in 1928 [2], provides away to measure molecular composition through inelastic scattering. The frequencyshift of the scattered light is a direct measure of the vibrational frequency (i.e. energy) of the molecule. Each molecule has its own distinct vibrational frequency orfrequencies. The frequency spectrum of the Raman-scattered light thus provides aunique fingerprint of the molecule. The Raman spectrum of material with multipleconstituents can thus be used to determine its molecular composition.A Raman spectrum consists of scattered intensity plotted vs. energy, or frequency,as shown in Fig. 12.2 for glucose in water. Each peak corresponds to a given Raman shift from the incident light energy hνL . The energy difference between the

Quantitative biological Raman spectroscopy367FIGURE 12.1: Energy diagram for Rayleigh, Stokes Raman, and anti-Stokes Raman scattering.initial and final vibrational states, hνV , the Raman shift νV , is usually measured inwavenumbers (cm 1 ), and is calculated as νV /c. Raman shifts from a given moleculeare always the same, regardless of the excitation frequency (or wavelength). Thisprovides flexibility in selecting a suitable laser excitation wavelength for a specificapplication.Infrared (IR) absorption, which probes vibrational structure in the energy range400–4000 cm 1 (25–2.5 µ m wavelength range), is also indicative of molecular vibrations. However, these wavelengths are not readily transmitted by most materials. Raman spectroscopy and IR absorption both probe the vibrational structure ofmolecules, and in many cases the same vibrations are observed. IR absorption is sensitive to vibrational frequencies that change the permanent dipole of the molecule.Raman scattering measures vibrational frequencies that result in a change of polarizability.Near-infrared (NIR) absorption spectroscopy probes the energy range from 4000to 10000 cm 1 (2.5–1 µ m wavelength range), where overtone and combinationbands of molecular vibrations occur. Such transitions are quantum mechanically“forbidden,” and are significantly weaker, and with broader features, than those observed in IR absorption. However, in contrast to IR absorption, shorter wavelengthNIR light is conveniently transmitted by common optical materials, conferring asubstantial advantage over IR absorption in instrumentation. As mentioned earlier,Raman shifts are independent of excitation wavelength, and thus there is flexibilityin choosing the wavelength range.

368Glucose optical sensing and impactFIGURE 12.2: A Raman spectrum consists of scattered intensity plotted vs. energy. This figure shows an aqueous glucose solution as an example.12.2 ReviewThis section briefly reviews the literature relevant to quantitative biological Ramanspectroscopy. Raman spectroscopy of biological tissue was initially demonstratedusing NIR Fourier transform Raman spectroscopy [3, 4]. In contrast to the visiblewavelength range, water absorption and background due to laser-induced autofluorescence are both smaller in the NIR, thus enabling deeper penetration depth andobservation of order-of-magnitude weaker Raman peaks. In its early developmentstages, Raman spectroscopy was primarily employed as a qualitative tool for chemical identification, with limited ability for quantification. Through the introductionand improvement of lasers, CCDs and other optical components, quantitative analysis became possible.In the following, we review three categories of work: semi-quantitative, univariate, and multivariate analyses. Such distinctions are made based on the types ofanalysis carried out. For instance, the hallmark of semi-quantitative work is normalization to the overall peak intensity. Although absolute intensity information is lostin the normalization step, quantitative analysis can be applied afterwards. Univariateanalysis uses one or a few characteristic peaks through measurement of peak heightsor integration of the area under the peaks.In contrast to univariate analysis, multivariate techniques are often called “fullspectral range” methods. This type of analysis is usually carried out when spectraloverlap exists, and therefore the characteristic peaks of interest are not obvious or are

Quantitative biological Raman spectroscopy369“contaminated” by adjacent features not belonging to the substance of interest. Asthe analysis becomes more sophisticated and more multivariate in nature, the issueof model robustness must be considered. We discuss various aspects of this topic inthe subsection implementationRaman spectroscopy has been employed in disease diagnosis using morphologicalmodels, with the rationale that characteristic morphological features are representative disease biomarkers. This approach is based on the unique correspondence between a particular morphological structure and the underlying chemical substance.These models are constructed via ordinary least squares (OLS) analysis, which assumes that the (important) spectral components are all precisely known, and thatthe observed experimental spectrum can be represented as a linear superposition ofthese spectral components, weighted by their concentrations [5]. Haka et al. [6]developed a morphological model for breast cancer diagnosis using confocal Ramanmicroscopy. They analyzed the Raman spectral features of normal, benign and malignant tissue samples in terms of the relative amount of collagen, fat, keratin, etc.Van de Poll et al. [7] and Buschman et al. [8] studied atherosclerosis using a similarapproach. Spectra of individual morphological structures were obtained using confocal Raman microscopy, and then applied to fit tissue spectra collected with an opticalfiber probe. In these studies, spectra of both the model components and those takenin tissue were normalized to their respective highest peaks, and absolute intensityinformation was not retained. However, the chemical composition could be quantified in terms of the relative proportions of the model components and then correlatedwith disease. For example, the relative quantity of collagen to fat was found to be arelevant breast cancer biomarker.12.2.2Univariate implementationFor some applications, characteristic and distinct Raman peaks of the chemical(molecule) of interest can be observed with little difficulty. Peak height measurement or integration of the area under the peak can be used as a quantitative indicatorof the substance. Caspers et al. [9] developed confocal Raman microscopy to perform non-invasive determination of the water profile in human skin in vivo. Petersonet al. [10] reported the acquisition of whole blood Raman spectra in vivo using tissuemodulation. Glucose concentrations were subsequently extracted from the area under particular spectral peaks of the whole blood spectra. A calibration model derivedfrom one individual was then used to generate meaningful predictions on independent data.12.2.3Multivariate implementationIn the Raman spectra of more complicated chemical systems, the various underlying components (called “interferents”) generally exhibit substantial spectral overlap.

370Glucose optical sensing and impactTherefore, no distinct Raman peak is available for peak height or area measurement,and the full spectrum must be used. This is called multivariate analysis. The goal ofmultivariate analysis is to obtain a spectrum of numbers, b( j), with j the wavelengthindex. When b( j) is projected onto an experimental spectrum s( j), one obtains accurate prediction of the analyte’s concentration, c [5]. Such spectra are often describedas column vectors, with each dimension corresponding to a given sampling point onthe wavelength axis. In these terms, c is obtained as the scalar product of b with theexperimental spectrum, b:c sT b(12.1)where lowercase boldface type denotes a column vector, and the superscript T denotes the transpose. Note that Eq. (12.1) assumes linearity, i.e., the observed spectrum can be represented as a linear superposition of underlying spectral components.Multivariate analysis proceeds in two steps. In calibration, one correlates known concentrations with spectra to obtain b. The resulting b, sometimes called the regressionvector, is then used to predict the concentration of an unknown sample. Multivariatecalibration is further discussed in detail in subsection 12.3.1, below.Non-invasive measurement of blood analyte concentrations is a widely pursuedtopic, and most studies employ multivariate techniques to extract analyte-specificconcentration information. However, from a data analysis standpoint multivariatecalibration presents more challenges than univariate methods, because of systemcomplexity and the resulting spectral overlap. Owing to its potential impact on diabetes, glucose has been often used as a model analyte.In vitro measurements of glucose have been performed in filtered blood serum [11,12], blood serum [13], and whole blood [14]. Rohleder et al. [12] discovered thatmeasurements from serum are greatly improved by ultrafiltration to remove macromolecules that cause intense Raman background and subsequently impair measurement accuracy. Results from whole blood were found to have greater error than thosefrom filtered or unfiltered serum, but were still within the clinically acceptable range.Lambert et al. [15] measured human aqueous humor, simulating measurements inthe eye, a convenient target for optical techniques. Our group studied glucose noninvasively in human subjects using Raman spectroscopy coupled with multivariateanalysis; Enejder et al. [16] accurately measured glucose concentrations in 17 nondiabetic volunteers following an oral glucose tolerance protocol. Results based onanalysis of spectra from individual and multiple volunteers indicated that the calibration model was based on glucose rather than spurious correlations.12.3 Quantitative Considerations for Raman SpectroscopyTraditionally, Raman spectroscopy has been utilized as an analytical tool for chemical identification and fingerprinting, where analysis has been based on observation

Quantitative biological Raman spectroscopy371of characteristic Raman peaks. As mentioned in the previous section, many morechallenges are encountered when Raman spectroscopy is used as a quantitative analytical tool. We discuss the challenges below.12.3.1Considerations for multivariate calibration modelsAs discussed previously, although Raman spectroscopy provides good molecularspecificity, spectral overlap is inevitable with the presence of multiple constituents.Since the glucose Raman signal is only 0.3% of the total skin Raman signal [17,18], and the spectrum is complicated by shot noise and varying fluorescence background, multivariate calibration is necessary. There are two types of multivariatetechniques, explicit and implicit. In explicit techniques such as OLS [5], the b vectoris calculated from the full set of known spectral components. In implicit techniques,such as partial least squares (PLS) [19, 20] analysis, the b vector is derived from acalibration data set composed of samples with known concentrations of the analyteof interest.Since multivariate calibration models are often built on an underdetermined dataset, careful assessment of model validity is required. Here we present some considerations for evaluating a calibration model. The reader is referred to the referencesfor more detailed information about multivariate calibration.12.3.2Fundamental and practical limitsIn spectroscopy, the amplitude of the Raman spectrum of the analyte of interestdepends on the number of analyte molecules sampled by the incoming light. The effective path length (in transmission mode) and sampling volume (in reflection mode)of the light are important parameters in estimating detection limits in turbid media. Modeling techniques such as diffusion theory [21] and Monte Carlo simulation[22] can be employed to calculate the fluence distribution inside the sample and theangular and radial profiles of the transmitted or reflected flux. Simulations withsynthetic data or experiments employing tissue-simulating physical models (called“phantoms”) can be of great value in determining how close the theoretical limitcan be realized in practice. In these studies, experimental conditions (e.g., signalto-noise ratio (SNR), instrumental drifts) and tissue phantom composition (e.g., interferents, concentrations) can be precisely controlled and well characterized in advance. Demonstrating that the chosen technique and instrument can measure physiological levels of the analyte of interest in phantoms is necessary but not sufficient tovalidate in vivo results. In vivo calibration models can only be validated by prospective studies.12.3.3Chance or spurious correlationMultivariate calibration algorithms are powerful, yet can be misleading if usedwithout caution. Owing to the nature of the underdetermined data set, minute correlations present in the data set can be misinterpreted by the algorithm as actual

372Glucose optical sensing and impactanalyte-specific variations. For example, Arnold et al. [23] measured the NIR absorption spectra of tissue phantoms devoid of glucose, and used temporal glucoseconcentration profiles published by different research groups to demonstrate that thecalibration model could produce an apparent correlation with glucose even thoughnone was present. It is important to note that calibration results such as these satisfiedmultiple criteria for judging the validity of a calibration model.Overfitting is another cause for spurious correlations. In multivariate calibration,a large number of sample spectra can be reduced to fewer factors. In practice, onlya subset of factors is significant in modeling the underlying analyte variations, whileothers are more likely to be dominated by noise and measurement errors. Althoughan apparently lower calibration error may be obtained by including more factorsin the calibration model, the reduction in error may be fortuitous and the resultingmodel may have less predictive capability.The lesson here is that chance or spurious correlations may be inadvertently incorporated in the calibration model even when rigorous validation procedures have beenfollowed. Additionally, if these chance or spurious correlations exist in prospectivedata, even good prediction results can be based on non-analyte-specific effects. Incorporating prior or additional information into the calibration model has been shownto provide more immunity to chance correlations [24–27].12.3.4Spectral evidence of the analyte of interestThe difficulty in visualizing analyte-specific information in biological spectra makesit challenging to verify the origin of the spectral information used by the c

Quantitative biological Raman spectroscopy 367 FIGURE 12.1: Energy diagram for Rayleigh, Stokes Raman, and anti-Stokes Ra-man scattering. initial and final vibrational states, hνV, the Raman shift νV, is usually measured in wavenumbers (cm¡1), and is calculated as νV c. Raman shifts from a given molecule are always the same, regardless of the excitation frequency (or wavelength).

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