Home | About | Journals | Submit | Contact Us | Français |

**|**HHS Author Manuscripts**|**PMC2840632

Formats

Article sections

- Abstract
- 1. Introduction
- 2. Theory
- 3. Methods
- 4. Results and discussion
- 5. Conclusion
- References and links

Authors

Related links

Opt Express. Author manuscript; available in PMC 2010 March 17.

Published in final edited form as:

PMCID: PMC2840632

NIHMSID: NIHMS106434

G. R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

The publisher's final edited version of this article is available at Opt Express

See other articles in PMC that cite the published article.

We present a novel technique, intrinsic Raman spectroscopy (IRS), to correct turbidity-induced Raman spectral distortions, resulting in the intrinsic Raman spectrum that would be observed in the absence of scattering and absorption. We develop an expression relating the observed and intrinsic Raman spectra through diffuse reflectance using the photon migration depiction of light transport. Numerical simulations are employed to validate the theoretical results and study the dependence of this expression on sample size and elastic scattering anisotropy.

Sample-to-sample turbidity variations are a limiting factor in non-invasive optical techniques. Macroscopically, light propagation in turbid media such as biological tissue is governed by elastic scattering and absorption of the media. For example, prominent absorption features of hemoglobin can lead to spectral shape distortions in tissue fluorescence spectroscopy [1–5], which subsequently confound interpretation of underlying fluorophores. Similarly, in diffuse reflectance and Raman spectroscopy, turbidity variations can cause sampling volume variations across samples [6–11]. Such turbidity-induced sampling volume variations introduce additional non analyte-specific variance into subsequent data analysis. This additional variance results in increased prediction error of analyte concentrations and a calibration algorithm that is not robust.

Many researchers have developed methods to correct for spectral distortions in biological fluorescence spectroscopy in which the shape of the observed spectrum is significantly altered by the presence of absorbers such as hemoglobin [3, 12–14]. Our laboratory has utilized diffuse reflectance spectroscopy (DRS) in the development of intrinsic fluorescence spectroscopy (IFS) to correct for turbidity distortions, particularly, absorption-induced spectral distortions of the fluorescence line shape [1, 2, 5]. Diffusely reflected light is the backward emission which undergoes numerous elastic scattering events before re-emerging from the tissue, and thereby provides a metric for the amount of tissue absorption and scattering present. The optical properties of a given sample at a particular wavelength can therefore be measured *in situ* by monitoring the diffuse reflectance at that wavelength. Similarly, DRS can monitor optical properties at multiple wavelengths. By measuring fluorescence and diffuse reflectance at the excitation wavelength and over the fluorescence emission wavelengths using the same excitation-collection geometry, the method of IFS can be used to remove these distortions. The underlying principle is that in a turbid medium fluorescence excitation-emission undergoes similar scattering and absorption as diffuse reflectance. For IFS, the main goal is to remove spectral shape distortions, exemplified by the hemoglobin absorption peak near 420 nm.

We are developing quantitative biological Raman spectroscopy to measure analyte concentrations in the near infrared (NIR) wavelength range (~ 830–1000 nm) [15]. In these studies, shape distortion is less of an issue because of the lack of absorbers with prominent spectral features in the NIR wavelength range [16]. However, for quantitative analysis, turbidity-induced sampling volume variations become very significant. Consider, for example, two identical biological tissue samples containing a Raman analyte, except that the second sample has a larger scattering coefficient than the first. The increased scattering causes light to be localized in a smaller volume, with a corresponding higher efficiency for the collection lens. As a result, the size of the Raman signal in the second sample will be larger than that of the first, and the measured concentration of the Raman analyte will be different. Furthermore, since both samples have some degree of scattering, the measured Raman concentration in both samples will differ from the actual concentration.

In the Raman spectroscopy literature, some researchers have applied corrections based on direct absorption spectroscopy [17–18]. Waters extended the formalism developed by Kubelka and Munk to relate the Raman spectrum to the measured diffuse reflectance as a function of either the Kubelka-Munk absorption or scattering coefficient [19]. This method assumes that only one optical property is changing at a time. Thus, for powdered samples, where the size of the particles and therefore their scattering characteristic change little over time, the effect of absorption from a progressively darkening sample on the Raman spectrum can be sufficiently removed [20–21]. However, the Kubelka-Munk formalism is not generally applicable to biological tissue because it assumes isotropic scattering, and biological tissue scattering is known to be anisotropic [22]. Recently, a method of retrieving Raman spectra from subsurface layers in diffusely scattering media was implemented, in which Raman scattered light from surface regions laterally offset from the excitation laser spot was collected and analyzed via multivariate techniques [23]. However, correction for sampling volume was not considered.

Under the photon migration framework developed by Wu *et al.* [1, 24], the same general principle that applies for IFS should hold true for Raman spectroscopy as well. The goal of this paper is to present a method which corrects measured analyte concentrations for turbidity-induced sampling volume variations. We refer to this method as intrinsic Raman spectroscopy (IRS). Starting from the photon migration theory, we review the analytical model for extracting intrinsic fluorescence (the fluorescence as it would be observed in the absence of scattering and absorption) and derive a parallel expression for the intrinsic Raman spectrum. Monte Carlo simulations are then employed to demonstrate its validity and elucidate the relationship between observed Raman and diffuse reflectance for semi-infinite samples and samples of finite dimension. An analysis of the methodology with respect to sample size and scattering anisotropy is presented. An experimental study is presented in the companion paper to validate this method and demonstrate that it can be used experimentally to correct for turbidity-induced spectral distortions and sampling volume variations.

Most analytical and numerical models of light propagation in tissue employ macroscopic optical properties, including the absorption coefficient, μ* _{a}* (cm

Light propagation in turbid media can be described by the radiative transfer equation [25]. However, the analytical solution to this integro-differential equation can be found only for very special conditions, with approximations. Diffusion theory is one of the most extensively studied approximations. The diffusion equation, along with appropriate boundary conditions dictated by the sample geometry, may be solved to provide the fluence distribution inside the sample and the reflected flux. Diffusion theory is often used to model photons that experience multiple scattering events and thus propagate “diffusively”, usually with a certain amount of source-detector separation [25].

Photon migration theory, developed by Wu *et al.* [24] employs probabilistic concepts to describe the scattering of light and to set up a framework that allows the calculation of the diffuse reflectance from semi-infinite turbid media. In this framework the diffuse reflectance from a semi-infinite medium can be written as:

$${R}_{d}={\displaystyle \sum _{n=1}^{\infty}{f}_{n}\left(g\right){a}^{n},}$$

(1)

with *f _{n}(g)* the photon escape probability distribution,

$${R}_{d}={\displaystyle \underset{0}{\overset{\infty}{\int}}{a}^{n}k\left(g\right){e}^{-k\left(g\right)n}dn=\frac{1}{1-\frac{\text{ln}a}{k\left(g\right)}},}$$

(2)

with *k(g)* an anisotropy and geometry dependent parameter that can be expressed as the product *S(1-g)* where *S* depends on the excitation-collection geometry. This quantity must be calibrated for each experiment. As demonstrated by Zonios *et al.* [26], this expression models the experimental results well.

Using photon migration theory, Wu *et al.* [1] derived an analytical expression relating the observed fluorescence (*F _{OBS}*) and the diffuse reflectance (

Following Wu’s derivation, the observed Raman spectrum (*Ram _{OBS}*) at various turbidities can be written as:

$$\begin{array}{l}{\mathit{\text{Ram}}}_{\mathit{\text{OBS}}}={\displaystyle \sum _{n=1}^{\infty}{f}_{n}\left(g\right)\{{\displaystyle \sum _{m=0}^{n-1}{a}_{x}^{m}\frac{{\mu}_{sR}}{{\mu}_{t}}{a}_{R}^{n-m-1}}\}}\hfill \\ =\frac{{\mathit{\text{Ram}}}_{\mathit{\text{INT}}}}{{\mu}_{t}l}\frac{{R}_{d,x}-{R}_{d,R}}{{a}_{x}-{a}_{R}}\hfill \end{array},$$

(3)

with μ* _{sR}* the Raman scattering coefficient, μ

$${\mathit{\text{Ram}}}_{\mathit{\text{INT}}}=\left({\mu}_{t}l\right){\mathit{\text{Ram}}}_{\mathit{\text{OBS}}}\frac{{a}_{x}-{a}_{R}}{{R}_{d,x}-{R}_{d,R}}.$$

(4)

Equation (4) can be further simplified to relate the observed Raman spectrum to the product of diffuse reflectance using the integral form in Eq. (2) under the restriction that μ* _{s}*>>μ

$${\mathit{\text{Ram}}}_{\mathit{\text{INT}}}=k\left(g\right)\frac{\left({\mu}_{t}l\right){\mathit{\text{Ram}}}_{\mathit{\text{OBS}}}}{{R}_{d,x}{R}_{d,R}}.$$

(5)

From this expression, the intrinsic Raman spectrum must be related to the observed Raman spectrum through a calibration procedure. In intrinsic fluorescence spectroscopy the calibration is applied to each term, *k(g)*, *R _{d,x}*, and

$${\mathit{\text{Ram}}}_{\mathit{\text{INT}}}=\frac{{\mu}_{t}}{f\left({R}_{d}\right)}{\mathit{\text{Ram}}}_{\mathit{\text{OBS}}}.$$

(6)

We call *f(R _{d})* the

In the following, Monte Carlo simulations are employed to elucidate the relationship between the observed Raman and the intrinsic Raman spectra. We also study the dependence of this calibration function on sample size and scattering anisotropy.

The Monte Carlo code employed here is based on an existing open source code developed by Jacques [28] for diffuse reflectance and fluorescence in a single layer medium. The code has two steps: In the first step, photons are injected from the top surface of the sample and propagate in the presence of elastic scattering and absorption. The absorbed quantity at each bin is recorded and used as the initial photon weight for the second step, in which fluorescence photons are launched from each bin isotropically and then propagated. The outcome includes diffuse reflectance, from the first step, and fluorescence, from the second step. A few modifications were made in our code: (1) A fixed-weight scheme was employed for photon weight bookkeeping, *i.e.*, the weight (intensity) of a photon stays the same as long as it is not absorbed or Raman scattered; when absorption or Raman scattering occurs, the photon weight is reduced to zero. This approach is similar to that of Welch *et al.* [29] and gives comparable results to Jacques’ albedo-based approach, but is perhaps more representative of a natural process. (2) Secondary Raman scattering is neglected, *i.e.*, a Raman photon cannot generate another Raman photon. This is a good assumption, since Raman scattering is a very rare event. (3) Angular resolution for the exiting flux was added and we provide for finite sample size. This allows us to compare results from different numerical apertures as well as various sample sizes. Cylindrical coordinates have been employed in the Monte Carlo code, thus the sample geometry reported in the format of radius by depth.

The simulation begins with injection of a photon into the medium with a calculated step size sampled from the probability distribution *p _{x}*=μ

A series of Monte Carlo simulations were performed. The goal was to study the relationship between Raman scattering and diffuse reflectance under various turbidity conditions. We simulated 49 samples, following a 7×7 matrix of scattering and absorption properties with ranges similar to those found in biological tissue [22], in which scattering usually dominates absorption. The scattering coefficient, μ* _{s}*, was varied from 18.4 to 99.4 cm

Using the Monte Carlo code described above, we studied the relationship between the observed and the intrinsic Raman spectra in two scenarios: semi-infinite and non-semi-infinite sample geometries, at a single Raman wavelength. From the simulation results, qualitatively we observe that Raman intensity changes with the diffuse reflectance, supporting the basic principle that both of them experience similar turbidity-induced distortions.

The one-to-one relationship between the observed fluorescence intensity and the diffuse reflectance intensity has been demonstrated [5] with either μ* _{s}* or μ

Under the semi-infinite condition with all return light collected, the diffuse reflectance observed with various turbidities is well described by a function of the ratio μ* _{s}*/μ

Diffuse reflectance from the 49 samples versus μ_{s}/μ_{a} for a 2 cm (r) by 2 cm (z) cylinder with three collection spot radii: 2, 1, and 0.5 cm. *g* was kept constant (0.8).

Diffuse reflectance from the 49 samples versus μ_{s}/μ_{a} for a 0.5 cm (r) by 1 cm (z) cylinder with three collection spot radii: 0.5, 0.25, and 0.1 cm. *g* was kept constant (0.8).

It is important to note that although diffuse reflectance versus μ* _{s}*/μ

From Monte Carlo simulations we have learned that the curvature of the calibration function increases with the sample size. An analogous phenomenon can be observed in Fig. 7 when the anisotropy (*g*) is varied from 0.99 to 0.7. In the high anisotropy (*g*=0.99) case, the scattered light is highly forward directed, resulting in an effective path length much longer than in the low anisotropy case; the exponent appears smaller, as in the smaller (*i.e.*, non-semi-infinite) samples. Further, the fact that the relationship between *Ram _{OBS}μ_{t}* and

(*Ram*_{OBS}μ_{t}) versus *R*_{d} for four *g*’s: 0.99, 0.95, 0.9, and 0.7. (Fixed sample size 2 cm (r) by 2 cm (z) and collection radius 2 cm for all cases).

The effect of sample size and scattering anisotropy on the curvature of the calibration function can be studied collectively using the Monte Carlo results shown in Fig. 8. Consideration of these two parameters and the interplay between them is important for experimental design. For example, it is known that whole blood is highly forward scattering with μ* _{s}* > 300 cm

To apply the intrinsic Raman spectroscopy correction, one needs to know the total attenuation coefficient μ* _{t}*. In Eq. (6), when μ

Turbidity variation is one of the major limitations in non-invasive quantitative biological Raman spectroscopy. To overcome this limitation, we have developed the theory of intrinsic Raman spectroscopy and provided validation using numerical simulations. We employed the photon migration theory for light propagation in turbid media, and related the intrinsic and the observed Raman spectra through diffuse reflectance. We employed Monte Carlo simulation to validate the modeling results and study the influence of sample geometry and scattering anisotropy on the curvature between the intrinsic and the observed Raman spectra. These results provide a systematic way to correct turbidity-induced sampling volume variations in NIR quantitative biological Raman spectroscopy. An immediate benefit of intrinsic Raman spectroscopy is the improvement in non-invasive determination of analyte concentrations in turbid media. The companion paper presents an experimental study to validate this method and demonstrate that it can be used experimentally to correct for turbidity-induced sampling volume variations.

This work was performed at the MIT Laser Biomedical Research Center and supported by the NIH National Center for Research Resources, grant P41-RR02594, and a grant from Bayer Health Care, LLC. Wei-Chuan Shih was a MIT Martin Fellow for Sustainability. We thank Ishan Barman, Gajendra Singh, and Ramachandra Dasari for valuable discussions.

**OCIS codes:** (170.1470) Blood or tissue constituent monitoring; (170.3660) Light propagation in tissue; (170.5280) Photon migration; (170.5660) Raman spectroscopy; (170.7050) Turbid media.

1. Wu J, Feld MS, Rava RP. Analytical model for extracting intrinsic fluorescence in turbid media. Appl. Opt. 1993;32:3585–3595. [PubMed]

2. Zhang QG, Muller MG, Wu J, Feld MS. Turbidity-free fluorescence spectroscopy of biological tissue. Opt. Lett. 2000;25:1451–1453. [PubMed]

3. Zhadin NN, Alfano RR. Correction of the internal absorption effect in fluorescence emission and excitation spectra from absorbing and highly scattering media: Theory and experiment. J. Biomed. Opt. 1998;3:171–186. [PubMed]

4. Gardner CM, Jacques SL, Welch AJ. Fluorescence spectroscopy of tissue: Recovery of intrinsic fluorescence from measured fluorescence. Appl. Opt. 1996;35:1780–1792. [PubMed]

5. Muller MG, Georgakoudi I, Zhang QG, Wu J, Feld MS. Intrinsic fluorescence spectroscopy in turbid media: disentangling effects of scattering and absorption. Appl. Opt. 2001;40:4633–4646. [PubMed]

6. Weersink R, Patterson MS, Diamond K, Silver S, Padgett N. Noninvasive measurement of fluorophore concentration in turbid media with a simple fluorescence/reflectance ratio technique. Appl. Opt. 2001;40:6389–6395. [PubMed]

7. Arnold MA, Small GW. Noninvasive glucose sensing. Anal. Chem. 2005;77:5429–5439. [PubMed]

8. Cote GL, Lec RM, Pishko MV. Emerging biomedical sensing technologies and their applications. IEEE Sens. J. 2003;3:251–266.

9. Khalil OS. Spectroscopic and clinical aspects of noninvasive glucose measurements. Clin. Chem. 1999;45:165–177. [PubMed]

10. Diamond KR, Farrell TJ, Patterson MS. Measurement of fluorophore concentrations and fluorescence quantum yield in tissue-simulating phantoms using three diffusion models of steady-state spatially resolved fluorescence. Phys. Med. Biol. 2003;48:4135–4149. [PubMed]

11. Pogue BW, Burke G. Fiber-optic bundle design for quantitative fluorescence measurement from tissue. Appl. Opt. 1998;37:7429–7436. [PubMed]

12. Patterson MS, Pogue BW. Mathematical-model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissue. Appl. Opt. 1994;33:1963–1974. [PubMed]

13. Biswal NC, Gupta S, Ghosh N, Pradhan A. Recovery of turbidity free fluorescence from measured fluorescence: an experimental approach. Opt. Express. 2003;11:3320–3331. [PubMed]

14. Finlay JC, Foster TH. Recovery of hemoglobin oxygen saturation and intrinsic fluorescence with a forward-adjoint model. Appl. Opt. 2005;44:1917–1933. [PubMed]

15. Enejder AMK, Scecina TG, Oh J, Hunter M, Shih WC, Sasic S, Horowitz GL, Feld MS. Raman spectroscopy for noninvasive glucose measurements. J. Biomed. Opt. 2005;10:031114. [PubMed]

16. Shih W-C, Bechtel KL, Feld MS. Constrained regularization: Hybrid method for multivariate calibration. Anal. Chem. 2007;79:234–239. [PubMed]

17. Nijhuis TA, Tinnemans SJ, Visser T, Weckhuysen BM. Operando spectroscopic investigation of supported metal oxide catalysts by combined time-resolved UV-VIS/Raman/on-line mass spectrometry. Phys. Chem. Chem. Phys. 2003;5:4361–4365.

18. Aarnoutse PJ, Westerhuis JA. Quantitative Raman reaction monitoring using the solvent as internal standard. Anal. Chem. 2005;77:1228–1236. [PubMed]

19. Waters DN. Raman spectroscopy of powders - effects of light absorption and scattering. Spectrochim. Acta, Part A. 1994;50:1833–1840.

20. Kuba S, Knozinger H. Time-resolved in situ Raman spectroscopy of working catalysts: sulfated and tungstated zirconia. J. Raman Spectrosc. 2002;33:325–332.

21. Tinnemans SJ, Kox MHF, Nijhuis TA, Visser T, Weckhuysen BM. Real time quantitative Raman spectroscopy of supported metal oxide catalysts without the need of an internal standard. Phys. Chem. Chem. Phys. 2005;7:211–216. [PubMed]

22. Tuchin VV. Tissue optics: light scattering methods and instruments for medical diagnosis. Bellingham, Wash: SPIE Press; 2000.

23. Matousek P, Clark IP, Draper ERC, Morris MD, Goodship AE, Everall N, Towrie M, Finney WF, Parker AW. Subsurface probing in diffusely scattering media using spatially offset Raman spectroscopy. Appl. Spectrosc. 2005;59:393–400. [PubMed]

24. Wu J, Partovi F, Field MS, Rava RP. Diffuse reflectance from turbid media - an analytical model of photon migration. Appl. Opt. 1993;32:1115–1121. [PubMed]

25. Ishimaru A. Wave propagation and scattering in random media. New York: Academic Press; 1978.

26. Zonios G, Dimou A. Modeling diffuse reflectance from semi-infinite turbid media: application to the study of skin optical properties. Opt. Express. 2006;14:8661–8674. [PubMed]

27. Shih W-C, Bechtel KL, Feld MS. Biomedical Optics. Optical Society of America; 2006. Intrinsic Raman spectroscopy improves analyte concentration measurements in turbid media; p. MC7.

28. Mycek M-A, Pogue BW. Handbook of biomedical fluorescence. New York, NY: Marcel Dekker; 2003.

29. Welch AJ, Gardner C, Richards-Kortum R, Chan E, Criswell G, Pfefer J, Warren S. Propagation of fluorescent light. Lasers Surg. Med. 1997;21:166–178. [PubMed]

30. Jacques SL. Diffuse reflectance from a semiinfinite medium. 1999. http://omlc.ogi.edu/news/may99/rd/index.html.

31. Fabbri F, Franceschini MA, Fantini S. Characterization of spatial and temporal variations in the optical properties of tissuelike media with diffuse reflectance imaging. Appl. Opt. 2003;42:3063–3072. [PubMed]

32. Zonios G, Perelman LT, Backman VM, Manoharan R, Fitzmaurice M, Van Dam J, Feld MS. Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo. Appl. Opt. 1999;38:6628–6637. [PubMed]

33. Wilson BC, Jacques SL. Optical reflectance and transmittance of tissues - principles and applications. IEEE J. Quantum Electron. 1990;26:2186–2199.

34. Roggan A, Friebel M, Dorschel K, Hahn A, Muller G. Optical properties of circulating human blood in the wavelength range 400–2500 NM. J. Biomed. Opt. 1999;4:36–46. [PubMed]

35. Farrell TJ, Patterson MS, Wilson B. a diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo. Med. Phys. 1992;19:879–888. [PubMed]

36. Dam JS, Pedersen CB, Dalgaard T, Fabricius PE, Aruna P, Andersson-Engels S. Fiber-optic probe for noninvasive real-time determination of tissue optical properties at multiple wavelengths. Appl. Opt. 2001;40:1155–1164. [PubMed]

37. Doornbos RMP, Lang R, Aalders MC, Cross FW, Sterenborg HJCM. The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy. Phys. Med. Biol. 1999;44:967–981. [PubMed]

38. Nichols MG, Hull EL, Foster TH. Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of optical properties of highly scattering systems. Appl. Opt. 1997;36:93–104. [PubMed]

PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers. |