OSA's Digital Library

Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 3, Iss. 1 — Jan. 1, 2012
  • pp: 137–152
« Show journal navigation

Semi-empirical model of the effect of scattering on single fiber fluorescence intensity measured on a turbid medium

S. C. Kanick, D. J. Robinson, H. J. C. M. Sterenborg, and A. Amelink  »View Author Affiliations


Biomedical Optics Express, Vol. 3, Issue 1, pp. 137-152 (2012)
http://dx.doi.org/10.1364/BOE.3.000137


View Full Text Article

Acrobat PDF (854 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Quantitative determination of fluorophore content from fluorescence measurements in turbid media, such as tissue, is complicated by the influence of scattering properties on the collected signal. This study utilizes a Monte Carlo model to characterize the relationship between the fluorescence intensity collected by a single fiber optic probe (FSF) and the scattering properties. Simulations investigate a wide range of biologically relevant scattering properties specified independently at excitation (λx) and emission (λm) wavelengths, including reduced scattering coefficients in the range μs(λx) ∈ [0.1 – 8]mm−1 and μs(λm) ∈ [0.25 – 1] × μs(λx). Investigated scattering phase functions (P(θ)) include both Henyey-Greenstein and Modified Henyey-Greenstein forms, and a wide range of fiber diameters (df ∈ [0.2 – 1.0] mm) was simulated. A semi-empirical model is developed to estimate the collected FSF as the product of an effective sampling volume, and the effective excitation fluence and the effective escape probability within the effective sampling volume. The model accurately estimates FSF intensities (r=0.999) over the investigated range of μs(λx) and μs(λm), is insensitive to the form of the P(θ), and provides novel insight into a dimensionless relationship linking FSF measured by different df.

© 2011 OSA

1. Introduction

Detection and quantitation of fluorescence is important for many biomedical and clinical applications. The optical detection of fluorescent endogenous compounds [1

1. N. Thekkek, S. Anandasabapathy, and R. Richards-Kortum, “Optical molecular imaging for detection of Barrett’s-associated neoplasia,” World J. Gastroenterol. 17:53–62 (2011). [CrossRef] [PubMed]

] such as collagen and NADH, or exogenous compounds that include labelled markers, can be used for diagnostic purposes [2

2. V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods. 7:603–614 (2010). [CrossRef] [PubMed]

, 3

3. S.L. Gibbs-Strauss, J.A. O’Hara, S. Srinivasan, P.J. Hoopes, T. Hasan, and B.W. Pogue, “Diagnostic detection of diffuse glioma tumors in vivo with molecular fluorescent probe-based transmission spectroscopy,” Med. Phys. 36:974–983 (2009). [CrossRef] [PubMed]

]. The measurement of therapeutic compounds, such as photosensitizers used in photodynamic therapy [4

4. C. C. Lee, B. W. Pogue, R. R. Strawbridge, K. L. Moodie, L. R. Bartholomew, G. C. Burke, and P. J. Hoopes, “Comparison of photosensitizer (AIPcS2) quantification techniques: in situ fluorescence microsampling versus tissue chemical extraction,” Photochem. Photobiol. 74:453–460 (2001). [CrossRef] [PubMed]

, 5

5. J. C. Finlay, T. C. Zhu, A. Dimofte, D. Stripp, S. B. Malkowicz, T. M. Busch, and S. M. Hahn, “Interstitial fluorescence spectroscopy in the human prostate during motexafin lutetium-mediated photodynamic therapy,” Photochem. Photobiol. 82:1270–1278 (2006). [CrossRef] [PubMed]

], may provide insight into the pharmacokinetic distribution and pharmacodynamic activity in tissues of interest and may play a role in monitoring administered therapies [6

6. D. J Robinson, M. B. Karakulluku, B. Kruijt, S. C. Kanick, R. L. P. van Veen, A. Amelink, H. J. C. M. Sterenborg, M. J. H. Witjes, and I. B. Tan, “Optical spectroscopy to guide photodynamic therapy of head and neck tumors,” IEEE J. Sel. Top. Quantum Electron. 16:854–862 (2010). [CrossRef]

]. However, quantitation of fluorescence in tissue in vivo is complicated by the influence of the tissue optical properties on the collected fluorescence signal [7

7. A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21:166–178 (1997). [CrossRef] [PubMed]

]. Absorption by chromophores within the tissue causes attenuation that is (non-linearly) proportional to the absorption coefficient at the excitation and emission wavelengths. Scattering within tissue is known to have a complicated effect on fluorescence measurements: the properties at the excitation wavelength (λx) affect the delivered excitation light profile and the properties at the emission wavelength (λm) determine the likelihood that fluorescent emission photons propagate to the detector used in the measurement. In order to quantitatively analyze fluorescence in tissue, it is important to obtain an intrinsic fluorescence signal that is independent of the optical property effects [8

8. J. Wu, M. S. Feld, and R. P Rava, “Analytical model for extracting intrinsic fluorescence in turbid media,” Appl. Opt. 19:3585–3595 (1993). [CrossRef]

10

10. M. G. Müller, I. Georgakoudi, Q. Zhang, J. Wu, and M. S. Feld, “Intrinsic fluorescence spectroscopy in turbid media: disentangling effects of scattering and absorption,” Appl. Opt. 40:4633–4646 (2001). [CrossRef]

]. This approach would yield a quantity that is proportional to the product of the concentration and quantum yield of the fluorophore within the optically sampled volume, and would be comparable between measurements of samples with different background tissue optical properties.

To the best of the authors’ knowledge, there is currently no analytical or empirical description of the influence of scattering properties on the fluorescence intensity sampled by a single fiber. The present study investigates the detailed mechanisms associated with the influence of scattering properties on the SFFL intensity measured in a turbid medium, and develops a mathematical model to correct for these influences. This represents a first step towards a full correction of collected SFFL intensities for the influence of optical properties (i.e. both scattering and absorption). Monte Carlo (MC) simulations are used to investigate SFFL measurement of a wide range of scattering properties that are independently specified at excitation and emission wavelengths; simulations also included a wide range of fiber diameters. Simulated data are used to identify and characterize a semi-empirical model that expresses SFFL intensity as a function of a dimensionless scattering property (given as the product of scattering coefficient and fiber diameter). The resulting model is applicable to all investigated fiber diameters and provides insight into the physics underlying the SFFL measurement.

2. Methods

2.1. Monte Carlo model

The Monte Carlo (MC) code utilized in this study is a customized version of the MCML program [27

27. L. Wang, S. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Prog. Biomed. 47:131–146 (1995). [CrossRef]

] that is modified to emulate single fiber fluorescence measurements of a homogeneous turbid medium. The code allows independent specification of both the scattering coefficient (μs) and scattering phase function (P(θ)) at excitation (λx) and emission (λm) wavelengths. Excitation photons were initialized by selecting a location on the fiber face, which is modeled in contact with the turbid medium at the air/medium interface z = 0, and were launched into a direction within the fiber cone of acceptance, where the acceptance angle was given as Θa=asin(NAnmedium); both the location and the direction were sampled from uniform distributions. The index of refraction (n) of the medium and fiber were specified at 1.37 and 1.45, respectively, and were held constant between λx and λm. The numerical aperture (NA) of the fiber was set as 0.22. Reflection and refraction due to the index of refraction mismatch at the medium/fiber and the surrounding medium/air interface were calculated using the Fresnel equations and Snell’s law. This code simulated propagation of excitations photons by stochastically selecting step sizes (sn) from an exponential distribution weighted by μs(λx), and each scattering angle was selected from P(θ)(λx). At discrete points along each individual step, excitation photons were stochastically checked for a fluorescence event, with the probability given by eμafsn, where μaf is the specific absorption coefficient of the fluorophore. Stochastic absorption by the fluorophore resulted in an isotropic scattering event, and propagation of the emission photon was continued at the scattering properties at λm. Emission photons propagating within the turbid medium that cross the medium interfacial boundary at z = 0, were checked for contact with the fiber face; those in contact and traveling at an angle within the fiber cone of acceptance were collected, the rest were terminated. Excitation photons contacting the fiber face at any angle were terminated and did not contribute to the collected fluorescence intensity. This calculation returned the fraction of the number of collected fluorescence photons and the number of excitation photons for each simulation, calculated as:
FSFratioMC=TMPCTXPL
(1)
where TXPL is the total number of excitation photons launched and TMPC the total number of emission photons collected. Excitation and emission photons propagating within the medium far from the fiber face do not contribute to the collected fluorescence intensity and were terminated at a hemispherical limit from the fiber face of 10dfibμs; a limit that was confirmed to not influence model outputs for the range of optical properties investigated in this study. Model outputs of FSFratioMC were validated by comparison with previously published fluorescence intensities over a range of background optical properties [18

18. T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Light propagation in tissue during fluorescence spectroscopy with single-fiber probes,” IEEE J. Sel. Top. Quantum Electron. 7:1004–1012 (2001). [CrossRef]

].

During photon propagation, the photon positions were tracked in a discrete voxel grid to yield individual 2D(r,z) probability density profiles for all incident excitation photons, for all fluorescence emission photons, and a separate profile for all collected fluorescence photons. Specifically, the code generated 2D maps of the relative excitation light fluence (Φx(r,z) [m−2]), which is calculated as previously described [27

27. L. Wang, S. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Prog. Biomed. 47:131–146 (1995). [CrossRef]

], and of the photon probability density of fluorescence collected by the fiber (Fcol(r,z) [m−3]), which represents the spatial location of origin for all collected fluorescence photons [18

18. T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Light propagation in tissue during fluorescence spectroscopy with single-fiber probes,” IEEE J. Sel. Top. Quantum Electron. 7:1004–1012 (2001). [CrossRef]

]. Note that these quantities involve ratio calculations and do not depend on the number of launched excitation photons. From these maps, the dimensionless escape probability density profile of emission photons (H(r,z)=Fcol(r,z)μaf(r,z)Φx(r,z)), which is defined as the probability of emission photon collection per fluorescence photon generated, was calculated. Note that the fluorescence generated at a location (r,z) is proportional to the product of μaf(r,z) and Φx(r,z). These 2-D spatial profiles were used to calculate effective values for the volume sampled and the excitation fluence and escape probability within the sampled volume, by properly weighting each respective quantity by the collected fluorescence that originated at the corresponding location. A scalar effective optical sampling depth (〈ZMC〉 [m]) is calculated as the weighted average depth of the collected emission photons, given as
ZMC=i=1nzzi(j=1nrFcol(rj,zi)Δaj)Δzi=1nz(j=1nrFcol(rj,zi)Δaj)Δz
(2)
where Δaj is the area of a voxel at position rj and Δz is the z-dimensional length of each voxel [27

27. L. Wang, S. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Prog. Biomed. 47:131–146 (1995). [CrossRef]

]. A scalar effective excitation fluence within the optically sampled volume (ΦxMC[m2]) was calculated from the weighted average of Φx(r,z), with the collected fluorescence photon probability density Fcol(r,z) as weight factors, as
ΦxMC=i=1nz(j=1nrΦx(rj,zi)Fcol(rj,zi)Δaj)Δzi=1nz(j=1nrFcol(rj,zi)Δaj)Δz
(3)
Similarly, a scalar for the effective escape probability within the optically sampled volume (HmMC[]) was calculated from the weighted average of the escape probability density distribution Hm(r,z), with the collected fluorescence photon probability density Fcol(r,z) as weight factors, as
HmMC=i=1nz(j=1nrHm(rj,zi)Fcol(rj,zi)Δaj)Δzi=1nz(j=1nrFcol(rj,zi)Δaj)Δz
(4)

2.2. Monte Carlo simulations

MC simulations were performed over a broad range of biologically relevant [28

28. W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Electron. 26:2166–2185 (1990). [CrossRef]

] reduced scattering coefficient (μs) values that were individually specified at λx and λm, with: μs(λx) = [0.1,0.25,0.5,1,2,4,8] mm−1 and μs(λm) = [0.25,0.5,0.75,1.0] × μs(λx). This series of simulations was performed at all specified μs combinations using the Modified Henyey-Greenstein (MHG) PF [24

24. S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence,” Biomed. Opt. Express 2:1687–1702 (2011). [CrossRef] [PubMed]

] with the anisotropy specified as g1 = 0.9 and γ, which characterizes the first two moments of the phase function and is given as γ=1g21g1, was set as γ = 1.4.

A subset of simulations further investigated the influence of PF over a selected range of reduced scattering values, μs(λx) = [0.5,1,2] mm−1 and μs(λm) = [0.5,1.0] × μs(λx), using the Henyey-Greenstein (HG) PF with g1 = [0.5,0.9] and γ = [1.5,1.9] and the MHG PF with combinations of g1 = [0.8,0.9,0.95] and γ = [1.4,1.5,1.6,1.7,1.8,1.9].

Additionally, simulations investigated variations in NA from the baseline value of 0.22 over the range [0.1 – 0.4]. This subset of simulations was performed using the same scattering properties as the subset of simulations used to investigate the influence of PF.

Simulations of each possible combination of scattering properties were performed for a range of fiber diameters, with df = [0.2,0.4,0.6,1.0] mm. The absorption of the fluorophore was given as μaf=0.1mm1 in all simulations; this study did not consider absorption due to background chromophores. In total, the data presented in this study include 616 MC simulations, each launching at least 20 million photons.

2.3. Semi-empirical model of the single fiber fluorescence intensity

The fluorescence signal F (in units of Joules [J]) collected by a fiber optic probe is given by the integral [12

12. J. C. Finlay and T. H. Foster, “Recovery of hemoglobin oxygen saturation and intrinsic fluorescence with a forward-adjoint model,” Appl. Opt. 44:1917–1933 (2005). [CrossRef] [PubMed]

]
F=(λx/λm)μafQfVΦx(r)Hm(r)d3r
(5)
where Φx(r) [J m−2] is the excitation fluence, Hm(r) [−] is the escape probability of emission photons, μaf[m1] is the absorption coefficient of the fluorophore at the excitation wavelength, and Qf [−] is the fluorescence quantum yield. The ratio (λx/λm) accounts for the difference in photon energy between the emission and excitation wavelengths, and will be omitted in the remainder of the equations since in the Monte Carlo simulations this ratio is set to unity. The volume integral of ΦxHm is dependent on optical properties; however the intrinsic fluorescence, given by the product of μafQf is independent of optical properties and has dimensions [m−1].

As described in Section 2.1, the MC simulations used in this study were used to return information about how SFFL intensity and the effective terms presented in Eq. (10) are influenced by scattering properties at the excitation and emission wavelengths. Inspection of the simulated data led to the identification of candidate empirical expressions to describe each quantity; from these a set of equations was selected on the basis of fit quality and model simplicity, and is given as
ZMC=dfA2(μs,avgdf)A3
(11)
ΦxMC=df2B1e1B2(μs(λx)df)+1
(12)
HmMC=C1eC3C2(μs(λm)df)+1
(13)
where [A1,2,3, B1,2, C1,2,3] in Eqs. (1013) are fitted parameters. The effective sampling depth 〈ZMC〉 was observed to follow an exponential decay with respect to the product of μs,avg(λx,λm)df, where μs,avg(λx,λm) is calculated as the average of μs(λx) and μs(λm). The effective relative excitation fluence ΦxMC was observed to scale with df2 as expected, and to follow an exponential expression that depended on the product μs(λx)df. The effective escape probability HmMC was observed to follow an exponential function that dependent on the product μs(λm)df. Substituting Eqs. (1113) into Eq. (10) results in
FSFratioMCμafQfdfνn=ζ1(μs,avgdf)ζ2e(1ζ2(μs(λx)df)+1ζ3ζ2(μs(λm)df)+1)
(14)
where [ζ1,ζ2,ζ3] are fitted parameters. This represents a reduction from the parameter set specified in Eqs. (1013). Here, ζ1 represents the product of A1, A2, B1 and C1. Fitted parameters were estimated using a Levenberg-Marquardt algorithm coded into a Matlab script (version 2009a, MathWorks). Confidence intervals of the estimated parameters were calculated from the square root of the diagonal of the covariance matrix [29

29. A. Amelink, D. J. Robinson, and H. J. C. M. Sterenborg, “Confidence intervals on fit parameters derived from optical reflectance spectroscopy measurements,” J. Biomed. Opt. 13:05040144 (2008). [CrossRef]

]. During the model fit analysis, the estimated values for A3, B2 and C2 were observed to have overlapping 95% confidence intervals [29

29. A. Amelink, D. J. Robinson, and H. J. C. M. Sterenborg, “Confidence intervals on fit parameters derived from optical reflectance spectroscopy measurements,” J. Biomed. Opt. 13:05040144 (2008). [CrossRef]

], which led to the reduction of these terms to a single fitted parameter, ζ2. This substitution did not result in a significant increase in model residual error.

Continuing the description of the terms in Eq. (14), νn represents the influence of the index of refraction mismatch at z = 0 (between fiber/medium and the annular air/medium interfaces). This parameter was found to be dependent on df, and to follow the form: νn=11+ɛdf, with ɛ = 0.17mm−1. This form was identified from comparing simulations of the fiber surrounded by air with the fiber surrounded by a refractive index matching the fiber; this factor is analogous to offset factors described previously [11

11. Q. Zhang, M. G. Müller, J. Wu, and M. S. Feld, “Turbidity-free fluorescence spectroscopy of biological tissue,” Opt. Lett. 25:1451–1453 (2000). [CrossRef]

].

Equation (14) represents a fiber diameter dependent expression that relates fluorescence collected by a single fiber with diameter df that has been distorted by scattering at excitation and emission wavelengths, to the intrinsic fluorescence μafQf within the sampled turbid medium. For brevity, the quantity FSFsim[m] will be used throughout this manuscript to refer to the expression
FSFsim=FSFratioMCμafQfνn
(15)

3. Results

3.1. Influence of scattering properties and fiber diameter on FSFsim

3.1.1. Case I: μs(λx) = μs(λm)

MC simulations investigated the relationship between single fiber fluorescence and variations in μs, initially specified as equivalent at λx and λm, and varied over the range [0.1 – 8.0] mm−1. Figure 1 A and B shows FSFsim collected by single fiber probes with df ∈ [0.2 – 1.0] mm. These data show a fiber-diameter specific nonlinear relationship between FSFsim and μs. Inspection of FSFsim data sampled by the df = 0.2 mm fiber shows a 60% decrease in intensity as μs increases across the investigated range. However, the df = 1.0 mm fiber shows an initial decrease in FSFsim of 25% as μs increases from 0.1 to 0.5 mm−1, and FSFsim then doubles in intensity as μs increases from 0.5 to 8 mm−1.

Fig. 1 Effect of reduced scattering coefficient (equivalent at λx, λm) on single fiber fluorescence intensity. Linear and log scales of the data are presented in the following panel pairings: A and B show collected FSFsim vs. μs. C and D shift the x-axis to dimensionless reduced scattering μsdf. E and F shift the y-axis to a dimensionless form of fluorescence, as FSFratioMC/df.

3.1.2. Case II: μs(λx) ≥ μs(λm)

The data investigated in Figure 1 are for the case μs(λx) = μs(λm); however, in tissue, μs(λ) is understood to follow a wavelength-dependent expression (e.g. Mie or Rayleigh approximations) such that μs(λx) > μs(λm). MC simulations were used to investigate FSFsim for the case of independent variation of μs(λx) (range: [0.1 – 8.0] mm) and μs(λm) (specified as μs(λm) = [0.25,0.5,0.75,1.0]×μs(λx)). Figures 2 A and B show linear and log representations of the full FSFsim/df data set plotted vs. μs(λx)df. Here, stratification of FSFsim/df measurements at μs(λx)df values are attributable to the influence of μs(λm) on the collected intensity. These data show clear deviation of FSFsim/df from the smooth curve displayed in Figures 1 E and F due to the independent influence of both μs(λx) and μs(λm) on SFFL intensity.

Fig. 2 Effect of independent variation of μs(λx) and μs(λm) on dimensionless single fiber fluorescence intensity, FSFsim/df plotted vs μs(λx)df ; vertical stratification is due to influence of μs(λm) variation. Linear and log plots given on A and B, respectively.

3.2. Influence of scattering phase function on FSFsim

In tissue the exact form and wavelength-dependence of the PF is not well characterized. This study utilized a subset of MC simulations to investigate in detail the influence of PF on FSFsim, as described in Section 2.2. The FSFsim showed minimal influence from variation among different phase functions, with < 3% variation between FSFsim/df values returned from the 19 simulated PFs at each of the dimensionless reduced scattering values (data not shown). For simulations specifying different PFs at λx and λm, the simulated FSFsim values showed no observable difference if the PF were interchanged between the wavelengths. These results demonstrate that SFFL is insensitive to the form of the PF for all investigated scattering properties and fiber diameters.

3.3. Influence of fiber NA on FSFsim

This study utilized a subset of MC simulations to investigate in the influence of fiber NA on FSFsim, as described in Section 2.2. Simulated data showed that the effect of fiber NA on FSFsim is well approximated by an NA2 proportionality, with < 5% mean residual error between estimates of FSF measured by fibers of NA= [0.22] and NA= [0.1,0.4] in the investigated scattering range (data not shown), with increasing deviations associated with decreasing dimensionless reduced scattering values.

3.4. Investigation and modeling of factors underlying FSFsim dependence on scattering properties

MC simulations were used to investigate the dependence of optical sampling depth, excitation fluence, and emission escape probability within the sampled volume on μs(λx) and μs(λm) within the sampled medium; these quantities were calculated as described in Section 2.1. Figure 3A shows a dimensionless description of effective optical sampling depth, given here as 〈ZMC〉/df, plotted vs. μs,avgdf, with μs,avg calculated as the average of μs(λx) and μs(λm) for each measurement. These 〈ZMC〉/df data exhibit a power law that shows a decreasing relationship with increasing μs,avgdf, resulting in a 10-fold decrease over the investigated μs,avgdf range. This relationship is well-characterized by Eq. (11); fitting this equation to these data yielded estimated values for A2 = 0.71 ± 0.01 and A3 = 0.36 ± 0.01,and resulted in accurate estimates of 〈ZMC〉/df over the full range of investigated μs,avgdf values (r = 0.996); model predictions are visualized by the solid black line on the plot.

Fig. 3 A) Dimensionless sampling depth 〈ZMC〉/df vs. the product of average of reduced scattering coefficients at excitation and emission wavelengths, μs,avg and df. B) Excitation fluence within the sampled volume, ΦxMCdf2 vs. dimensionless reduced scattering at the excitation wavelength, μs(λx)df. C) Escape probability of emission photons, HmMC vs. dimensionless reduced scattering at the emission wavelength, μs(λm)df. Fitted model estimates visualized by solid black lines.

3.5. Semi-empirical model of FSFsim

Figure 4 shows FSFsim/df simulated by the MC model vs. estimated by the fit of Eq. (14). Here the estimated parameter values of ζ1 = 0.0935 ± 0.003, ζ2 = 0.31 ± 0.01, and ζ3 = 1.61 ± 0.05 resulted in the minimum weighted residual error between simulated and model-estimated FSFsim values. The model estimates were strongly correlated with simulated outputs, with the quality of the fit given by the Pearson correlation coefficient of r = 0.991 and displayed by the proximity of the data points to the plotted line of unity. The mean absolute residual between simulated and model estimated values is < 3% and all data points have a mean residual error that is < 10% of the simulated value. Figures 5A and B show simulated and model estimated FSFsim/df vs. μs(λx)df ; this plot visualizes the capability of the model to describe the influence of both μs(λx) and μs(λm) on the collected fluorescence intensity. These results indicate that Eq. (14) provides an accurate description of the SFFL intensity over a wide range of μs(λx), μs(λm), and df, and is valid for all investigated forms of the PF.

Fig. 4 Dimensionless single fiber fluorescence intensity estimated by fitted model vs. MC simulated values. Data include variations of μs(λx) and μs(λm). Line of unity included for comparative purposes.
Fig. 5 Dimensionless single fiber fluorescence intensity estimated by fitted model (× marks) and returned by MC simulations (○ marks). Data include independent variation of μs(λx) and μs(λm), and are plotted vs. μs(λx)df. Linear and log plots given on A and B, respectively.

4. Discussion

This study utilizes a Monte Carlo model to characterize the relationship between the fluorescence intensity collected by a single fiber (FSF) and the scattering properties within an optically sampled turbid medium. Simulated data were used to identify a relationship between dimensionless fluorescence intensity, FSFsim/df, and dimensionless reduced scattering. We found that the collected fluorescence does not scale exclusively with dimensionless reduced scattering at the excitation wavelength, nor with dimensionless reduced scattering at the emission wavelength; rather it shows a more-complicated dependence on the reduced scattering coefficients at both wavelengths. These data were used to develop a semi-empirical model that expresses FSFsim/df as the product of an effective sampling volume, and the effective excitation fluence and the effective escape probability within the effective sampling volume. The influence of scattering properties on each of these components was identified and mathematically described using simulation outputs. The semi-empirical model of FSFsim/df accurately describes simulated fluorescence intensities over a wide range of biologically relevant scattering properties.

4.1. Influence of scattering properties on FSFsim

Fig. 6 Dimensionless single fiber fluorescence intensity plotted vs. dimensionless reduced scattering calculated as A) mean of μs(λx) and μs(λm) and B) harmonic average expression including μs(λx) and μs(λm), given in Eqn 16. Smooth dependence of fluorescence intensity vs. these respective scattering parameters suggests region μsdf < 0.5 is dominated by volume effects, region μsdf > 0.5 is dominated by excitation fluence and emission probability within sampled volume.

4.2. Application of semi-empirical model of FSFsim to extract intrinsic fluorescence in turbid media

The semi-empirical model developed in this study provides a method to return scattering-independent FSF quantities provided that μs(λx) and μs(λm) are determined, e.g. from a white-light reflectance measurement. This approach is in contrast to other techniques that utilize raw reflectance to correct raw fluorescence for the influence of scattering properties. Such an approach is not appropriate for single fiber measurements, because reflectance intensities collected by single fibers (RSF) are not only sensitive to μs, but (in contrast to SFFL) are also heavily influenced by the PF [24

24. S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence,” Biomed. Opt. Express 2:1687–1702 (2011). [CrossRef] [PubMed]

, 31

31. F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source–detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16:2935–2945 (1999). [CrossRef]

, 32

32. A. Kienle, F. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26:1571–1573 (2001). [CrossRef]

]. Due to this difference in PF dependence of FSF and RSF, the ratio of these two quantities will also be PF dependent. The magnitude of this dependence can best be appreciated by considering RSF measurements of two (hypothetical) turbid media with μs values of 0.5 and 2.0 mm−1, both with the same intrinsic fluorescence, and measured by a fiber with df = 1.0 mm. If the PF within the two media were varied from γ = 1.9 to γ = 1.4 (a change that would increase the likelihood of large-angle scattering events), the resulting RSF would increase by a factor of 2.3 for μs = 0.5 mm−1 and a factor of 1.4 for μs = 2.0 mm−1 [24

24. S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence,” Biomed. Opt. Express 2:1687–1702 (2011). [CrossRef] [PubMed]

, 25

25. S. C. Kanick, U. A. Gamm, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Method to quantitatively estimate wavelength-dependent scattering properties from multi-diameter single fiber reflectance spectra measured in a turbid medium,” Opt. Lett. 36:2997–2999 (2011). [CrossRef] [PubMed]

]. For a smaller fiber of df = 0.2 mm, the effects are amplified to factors of 3.1 and 1.5 for each respective case. Importantly, the variation in PF would have a negligible effect on the raw FSF ; such a difference in sensitivity to PF is attributable to the isotropic release of emission photons during propagation of fluorescent light. In contrast to RSF, which relies on the likelihood of forward directed incident light to undergo a large-angle scattering event (defined by the PF), the isotropic release of a fluorescent photon greatly reduces the sensitivity of FSF to PF. Therefore, for single fiber measurements (and likely other geometries which collect light close to the source fiber), a fluorescence correction algorithm that utilized a ratio of FSF and RSF could result in inaccurate estimation of intrinsic fluorescence by up to a factor of > 3 for small dimensionless scattering values.

The PF-specific analysis presented in this study indicates that quantitative analysis of SFFL requires determination of μs(λx) and μs(λm) independent of PF. This could be achieved using a multi-diameter SFR measurement, as described recently by our group [25

25. S. C. Kanick, U. A. Gamm, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Method to quantitatively estimate wavelength-dependent scattering properties from multi-diameter single fiber reflectance spectra measured in a turbid medium,” Opt. Lett. 36:2997–2999 (2011). [CrossRef] [PubMed]

,26

26. U. A. Gamm, S. C. Kanick, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of tissue scattering properties using multi-diameter single fiber reflectance spectroscopy: in silico sensitivity analysis,” Biomed. Opt. Express 2:3150–3166 (2011). [CrossRef] [PubMed]

]. The MDSFR approach utilizes the γ-specific RSF vs. μsdf relationship for measurements using multiple fibers at each investigated wavelength. By specification of a background scattering model within the sampled tissue (e.g. Mie and or Rayleigh scattering) it is possible to determine μs and γ across the a range of wavelengths. Moreover, this calculation can be made in the presence of absorption from tissue chromophores, requiring only specification of the basis set of absorbing constituents and their respective specific absorption coefficients. This multi-fiber approach can be executed using as few as two optical fibers with different diameters [26

26. U. A. Gamm, S. C. Kanick, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of tissue scattering properties using multi-diameter single fiber reflectance spectroscopy: in silico sensitivity analysis,” Biomed. Opt. Express 2:3150–3166 (2011). [CrossRef] [PubMed]

]; moreover, such a device can easily be developed to sample both RSF and FSF. The combined multi-diameter SFR and SFFL would return paired local measurements of fluorescence and tissue optical properties within the same (shallow) sampling volume. Such a technique has the potential to provide clinically useful information for tissue diagnostics and monitoring of administered therapies. The localized measurement volume would allow quantitative characterization of heterogeneities in the spatial distribution of an administered fluorescent compound; this may be advantageous compared with a volume-averaged metric gained from diffuse optical measurements. Moreover, the measurement volume can be selected at a specific area of interest (e.g. in the center of an identified malignant area, or on the border between suspicious and normal tissue). This multi-fiber approach faces challenges that must be properly assessed, including proper identification of background scattering models for determination of μs(λ), the influence of μa on FSF, and the influence of heterogeneities on both RSF and FSF ; ongoing studies are investigating these issues.

4.3. Limitations and future work

In order to appropriately utilize the semi-empirical model of SFFL presented in this study, it is important to consider the assumptions and approximations utilized in its development. The mathematical modeling approach utilized in this study represents the collected fluorescence intensity in terms of the product of three factors contributing to fluorescence that were extracted from Monte Carlo models outputs; these relationships are presented in the transition from Equation 6 to 10. A critical assumption of this modeling approach is that the effective scalar values for these components are representative of the more complicated 2-D maps of these properties. The empirical models of each of the components expresses a high quality of fit, providing evidence that this assumption is reasonable. Another important point of this study is the specific investigation of a single optical fiber in contact with a turbid medium; the exact form of the expressions governing light transport have been defined for this geometry. While the approach to modeling SFFL utilized here is extensible to modifications in measurement geometry, it is important to note that changes to the geometry will result in changes to the excitation and emission light distributions, and will require assessment of the appropriateness and accuracy of the specified model structures. Such modifications include interstitial placement of the fiber optic in the sampled medium, or placement of the fiber optic into a probe face surrounded by epoxy, metal, or other optical fibers; ongoing work is investigating these influences. Another important consideration is that this study characterized the scattering dependence of FSF, and did not consider background absorption effects. Absorption within the sampled medium, at both excitation and emission wavelengths, is expected to have a substantial influence on the raw fluorescence intensity collected and the volume probed during measurement. Further complicating matters, the magnitude of the absorption attenuation is expected to be heavily influenced by the paired scattering properties at excitation and emission wavelengths. An ongoing study will characterize the influence of absorption on the individual components of the SFFL model. Additionally, the MC model utilized in this study was validated by comparison with model returned outputs reported in the literature; future work will conduct experimental validation in optical phantoms.

5. Conclusions

In summary, the current study utilized MC simulations to investigate the influence of scattering properties on fluorescence intensity collected by a single fiber probe. Simulated data were used to identify an underlying dimensionless relationship between fluorescence intensity and dimensionless reduced scattering. Results indicate that the mathematical model of FSF is valid over a wide range of reduced scattering coefficients, in the range μs(λx) ∈ [0.1 – 8] mm−1 and μs(λm) ∈ [0.25 – 1] × μs(λx), and scattering phase functions (P(θ)), with both Henyey-Greenstein and Modified Henyey-Greenstein forms with anisotropy in the range 0.5 – 0.95 and γ ∈ [1.4 – 1.9], and a wide range of fiber diameters (df ∈ [0.2 – 1.0] mm). The model accurately estimates FSF given μs(λx) and μs(λm), and is insensitive to the anisotropy and higher order moments of the PF. Results indicate that correction for the influence of scattering on FSF requires estimation of scattering optical properties from a paired measurement of white-light reflectance.

References and links

1.

N. Thekkek, S. Anandasabapathy, and R. Richards-Kortum, “Optical molecular imaging for detection of Barrett’s-associated neoplasia,” World J. Gastroenterol. 17:53–62 (2011). [CrossRef] [PubMed]

2.

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods. 7:603–614 (2010). [CrossRef] [PubMed]

3.

S.L. Gibbs-Strauss, J.A. O’Hara, S. Srinivasan, P.J. Hoopes, T. Hasan, and B.W. Pogue, “Diagnostic detection of diffuse glioma tumors in vivo with molecular fluorescent probe-based transmission spectroscopy,” Med. Phys. 36:974–983 (2009). [CrossRef] [PubMed]

4.

C. C. Lee, B. W. Pogue, R. R. Strawbridge, K. L. Moodie, L. R. Bartholomew, G. C. Burke, and P. J. Hoopes, “Comparison of photosensitizer (AIPcS2) quantification techniques: in situ fluorescence microsampling versus tissue chemical extraction,” Photochem. Photobiol. 74:453–460 (2001). [CrossRef] [PubMed]

5.

J. C. Finlay, T. C. Zhu, A. Dimofte, D. Stripp, S. B. Malkowicz, T. M. Busch, and S. M. Hahn, “Interstitial fluorescence spectroscopy in the human prostate during motexafin lutetium-mediated photodynamic therapy,” Photochem. Photobiol. 82:1270–1278 (2006). [CrossRef] [PubMed]

6.

D. J Robinson, M. B. Karakulluku, B. Kruijt, S. C. Kanick, R. L. P. van Veen, A. Amelink, H. J. C. M. Sterenborg, M. J. H. Witjes, and I. B. Tan, “Optical spectroscopy to guide photodynamic therapy of head and neck tumors,” IEEE J. Sel. Top. Quantum Electron. 16:854–862 (2010). [CrossRef]

7.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21:166–178 (1997). [CrossRef] [PubMed]

8.

J. Wu, M. S. Feld, and R. P Rava, “Analytical model for extracting intrinsic fluorescence in turbid media,” Appl. Opt. 19:3585–3595 (1993). [CrossRef]

9.

C. M. Gardner, S. L. Jacques, and A. J. Welch, “Fluorescence spectroscopy of tissue: recovery of intrinsic fluorescence from measured fluorescence,” Appl. Opt. 35:1780–1792 (1996). [CrossRef] [PubMed]

10.

M. G. Müller, I. Georgakoudi, Q. Zhang, J. Wu, and M. S. Feld, “Intrinsic fluorescence spectroscopy in turbid media: disentangling effects of scattering and absorption,” Appl. Opt. 40:4633–4646 (2001). [CrossRef]

11.

Q. Zhang, M. G. Müller, J. Wu, and M. S. Feld, “Turbidity-free fluorescence spectroscopy of biological tissue,” Opt. Lett. 25:1451–1453 (2000). [CrossRef]

12.

J. C. Finlay and T. H. Foster, “Recovery of hemoglobin oxygen saturation and intrinsic fluorescence with a forward-adjoint model,” Appl. Opt. 44:1917–1933 (2005). [CrossRef] [PubMed]

13.

G. M. Palmer and N. Ramanujam, “Monte-carlo-based model for the extraction of intrinsic fluorescence from turbid media,” J. Biomed. Opt. 13:024017 (2008). [CrossRef] [PubMed]

14.

G. M. Palmer, R. J. Viola, T. Schroeder, P. S. Yarmolenko, M. W. Dewhirst, and N. Ramanujam, “Quantitative diffuse reflectance and fluorescence spectroscopy: tool to monitor tumor physiology in vivo,” J. Biomed. Opt. 14:024010 (2009). [CrossRef] [PubMed]

15.

R. H. Wilson, M. Chandra, J. Scheiman, D. Simeone, B. McKenna, J. Purdy, and M. A. Mycek, “Optical spectroscopy detects histological hallmarks of pancreatic cancer,” Opt. Express 17:17502–17516 (2009). [CrossRef] [PubMed]

16.

A. Kim, M. Khurana, Y. Moriyama, and B. C. Wilson, “Quantification of in vivo fluorescence decoupled from the effects of tissue optical properties using fiber-optic spectroscopy measurements,” J. Biomed. Opt. 15:067006 (2010). [CrossRef]

17.

B. W. Pogue and G. Burke, “Fiber-optic bundle design for quantitative fluorescence measurement from tissue,” Appl. Opt. 37: 7429–7436 (1998). [CrossRef]

18.

T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Light propagation in tissue during fluorescence spectroscopy with single-fiber probes,” IEEE J. Sel. Top. Quantum Electron. 7:1004–1012 (2001). [CrossRef]

19.

K. R. Diamond, M. S. Patterson, and T. J. Farrell, “Quantification of fluorophore concentration in tissue-simulating media by fluorescence measurements with a single optical fiber,” Appl. Opt. 42:2436–2442 (2003). [CrossRef] [PubMed]

20.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Medical Laser Application 22:23–34 (2007). [CrossRef]

21.

A. Amelink, B. Kruijt, D. J. Robinson, and H. J. C. M. Sterenborg, “Quantitative fluorescence spectroscopy in turbid media using fluorescence differential path length spectroscopy,” J. Biomed. Opt. 13:054051 (2008). [CrossRef] [PubMed]

22.

M. Sinaasappel and H. J. C. M. Sterenborg, “Quantification of the hematoporphyrin derivative by fluorescence measurement using dual-wavelength excitation and dual-wavelength detection,” Appl. Opt. 32:541–548 (1993). [CrossRef] [PubMed]

23.

R. Weersink, M. S. Patterson, K. Diamond, S. Silver, and N. Padgett, “Noninvasive measurement of fluorophore concentration in turbid media with a simple fluorescence /reflectance ratio technique,” Appl. Opt. 40:6389–6395 (2001). [CrossRef]

24.

S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence,” Biomed. Opt. Express 2:1687–1702 (2011). [CrossRef] [PubMed]

25.

S. C. Kanick, U. A. Gamm, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Method to quantitatively estimate wavelength-dependent scattering properties from multi-diameter single fiber reflectance spectra measured in a turbid medium,” Opt. Lett. 36:2997–2999 (2011). [CrossRef] [PubMed]

26.

U. A. Gamm, S. C. Kanick, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of tissue scattering properties using multi-diameter single fiber reflectance spectroscopy: in silico sensitivity analysis,” Biomed. Opt. Express 2:3150–3166 (2011). [CrossRef] [PubMed]

27.

L. Wang, S. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Prog. Biomed. 47:131–146 (1995). [CrossRef]

28.

W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Electron. 26:2166–2185 (1990). [CrossRef]

29.

A. Amelink, D. J. Robinson, and H. J. C. M. Sterenborg, “Confidence intervals on fit parameters derived from optical reflectance spectroscopy measurements,” J. Biomed. Opt. 13:05040144 (2008). [CrossRef]

30.

E. J. Hudson, M. R. Stringer, F. Cairnduff, D. V. Ash, and M. A. Smith, “The optical properties of skin tumours measured during superficial photodynamic therapy,” Laser. Med. Sci. 9:99–103 (1994). [CrossRef]

31.

F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source–detector separations close to one transport mean free path,” J. Opt. Soc. Am. A 16:2935–2945 (1999). [CrossRef]

32.

A. Kienle, F. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26:1571–1573 (2001). [CrossRef]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(290.7050) Scattering : Turbid media
(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence

ToC Category:
Optics of Tissue and Turbid Media

History
Original Manuscript: September 29, 2011
Revised Manuscript: November 11, 2011
Manuscript Accepted: November 11, 2011
Published: December 14, 2011

Citation
S. C. Kanick, D. J. Robinson, H. J. C. M. Sterenborg, and A. Amelink, "Semi-empirical model of the effect of scattering on single fiber fluorescence intensity measured on a turbid medium," Biomed. Opt. Express 3, 137-152 (2012)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-1-137


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. N. Thekkek, S. Anandasabapathy, and R. Richards-Kortum, “Optical molecular imaging for detection of Barrett’s-associated neoplasia,” World J. Gastroenterol.17:53–62 (2011). [CrossRef] [PubMed]
  2. V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods.7:603–614 (2010). [CrossRef] [PubMed]
  3. S.L. Gibbs-Strauss, J.A. O’Hara, S. Srinivasan, P.J. Hoopes, T. Hasan, and B.W. Pogue, “Diagnostic detection of diffuse glioma tumors in vivo with molecular fluorescent probe-based transmission spectroscopy,” Med. Phys.36:974–983 (2009). [CrossRef] [PubMed]
  4. C. C. Lee, B. W. Pogue, R. R. Strawbridge, K. L. Moodie, L. R. Bartholomew, G. C. Burke, and P. J. Hoopes, “Comparison of photosensitizer (AIPcS2) quantification techniques: in situ fluorescence microsampling versus tissue chemical extraction,” Photochem. Photobiol.74:453–460 (2001). [CrossRef] [PubMed]
  5. J. C. Finlay, T. C. Zhu, A. Dimofte, D. Stripp, S. B. Malkowicz, T. M. Busch, and S. M. Hahn, “Interstitial fluorescence spectroscopy in the human prostate during motexafin lutetium-mediated photodynamic therapy,” Photochem. Photobiol.82:1270–1278 (2006). [CrossRef] [PubMed]
  6. D. J Robinson, M. B. Karakulluku, B. Kruijt, S. C. Kanick, R. L. P. van Veen, A. Amelink, H. J. C. M. Sterenborg, M. J. H. Witjes, and I. B. Tan, “Optical spectroscopy to guide photodynamic therapy of head and neck tumors,” IEEE J. Sel. Top. Quantum Electron.16:854–862 (2010). [CrossRef]
  7. A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med.21:166–178 (1997). [CrossRef] [PubMed]
  8. J. Wu, M. S. Feld, and R. P Rava, “Analytical model for extracting intrinsic fluorescence in turbid media,” Appl. Opt.19:3585–3595 (1993). [CrossRef]
  9. C. M. Gardner, S. L. Jacques, and A. J. Welch, “Fluorescence spectroscopy of tissue: recovery of intrinsic fluorescence from measured fluorescence,” Appl. Opt.35:1780–1792 (1996). [CrossRef] [PubMed]
  10. M. G. Müller, I. Georgakoudi, Q. Zhang, J. Wu, and M. S. Feld, “Intrinsic fluorescence spectroscopy in turbid media: disentangling effects of scattering and absorption,” Appl. Opt.40:4633–4646 (2001). [CrossRef]
  11. Q. Zhang, M. G. Müller, J. Wu, and M. S. Feld, “Turbidity-free fluorescence spectroscopy of biological tissue,” Opt. Lett.25:1451–1453 (2000). [CrossRef]
  12. J. C. Finlay and T. H. Foster, “Recovery of hemoglobin oxygen saturation and intrinsic fluorescence with a forward-adjoint model,” Appl. Opt.44:1917–1933 (2005). [CrossRef] [PubMed]
  13. G. M. Palmer and N. Ramanujam, “Monte-carlo-based model for the extraction of intrinsic fluorescence from turbid media,” J. Biomed. Opt.13:024017 (2008). [CrossRef] [PubMed]
  14. G. M. Palmer, R. J. Viola, T. Schroeder, P. S. Yarmolenko, M. W. Dewhirst, and N. Ramanujam, “Quantitative diffuse reflectance and fluorescence spectroscopy: tool to monitor tumor physiology in vivo,” J. Biomed. Opt.14:024010 (2009). [CrossRef] [PubMed]
  15. R. H. Wilson, M. Chandra, J. Scheiman, D. Simeone, B. McKenna, J. Purdy, and M. A. Mycek, “Optical spectroscopy detects histological hallmarks of pancreatic cancer,” Opt. Express17:17502–17516 (2009). [CrossRef] [PubMed]
  16. A. Kim, M. Khurana, Y. Moriyama, and B. C. Wilson, “Quantification of in vivo fluorescence decoupled from the effects of tissue optical properties using fiber-optic spectroscopy measurements,” J. Biomed. Opt.15:067006 (2010). [CrossRef]
  17. B. W. Pogue and G. Burke, “Fiber-optic bundle design for quantitative fluorescence measurement from tissue,” Appl. Opt.37: 7429–7436 (1998). [CrossRef]
  18. T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Light propagation in tissue during fluorescence spectroscopy with single-fiber probes,” IEEE J. Sel. Top. Quantum Electron.7:1004–1012 (2001). [CrossRef]
  19. K. R. Diamond, M. S. Patterson, and T. J. Farrell, “Quantification of fluorophore concentration in tissue-simulating media by fluorescence measurements with a single optical fiber,” Appl. Opt.42:2436–2442 (2003). [CrossRef] [PubMed]
  20. H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Medical Laser Application22:23–34 (2007). [CrossRef]
  21. A. Amelink, B. Kruijt, D. J. Robinson, and H. J. C. M. Sterenborg, “Quantitative fluorescence spectroscopy in turbid media using fluorescence differential path length spectroscopy,” J. Biomed. Opt.13:054051 (2008). [CrossRef] [PubMed]
  22. M. Sinaasappel and H. J. C. M. Sterenborg, “Quantification of the hematoporphyrin derivative by fluorescence measurement using dual-wavelength excitation and dual-wavelength detection,” Appl. Opt.32:541–548 (1993). [CrossRef] [PubMed]
  23. R. Weersink, M. S. Patterson, K. Diamond, S. Silver, and N. Padgett, “Noninvasive measurement of fluorophore concentration in turbid media with a simple fluorescence /reflectance ratio technique,” Appl. Opt.40:6389–6395 (2001). [CrossRef]
  24. S. C. Kanick, U. A. Gamm, M. Schouten, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of the reduced scattering coefficient of turbid media using single fiber reflectance spectroscopy: fiber diameter and phase function dependence,” Biomed. Opt. Express2:1687–1702 (2011). [CrossRef] [PubMed]
  25. S. C. Kanick, U. A. Gamm, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Method to quantitatively estimate wavelength-dependent scattering properties from multi-diameter single fiber reflectance spectra measured in a turbid medium,” Opt. Lett.36:2997–2999 (2011). [CrossRef] [PubMed]
  26. U. A. Gamm, S. C. Kanick, H. J. C. M. Sterenborg, D. J. Robinson, and A. Amelink, “Measurement of tissue scattering properties using multi-diameter single fiber reflectance spectroscopy: in silico sensitivity analysis,” Biomed. Opt. Express2:3150–3166 (2011). [CrossRef] [PubMed]
  27. L. Wang, S. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comp. Meth. Prog. Biomed.47:131–146 (1995). [CrossRef]
  28. W. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quant. Electron.26:2166–2185 (1990). [CrossRef]
  29. A. Amelink, D. J. Robinson, and H. J. C. M. Sterenborg, “Confidence intervals on fit parameters derived from optical reflectance spectroscopy measurements,” J. Biomed. Opt.13:05040144 (2008). [CrossRef]
  30. E. J. Hudson, M. R. Stringer, F. Cairnduff, D. V. Ash, and M. A. Smith, “The optical properties of skin tumours measured during superficial photodynamic therapy,” Laser. Med. Sci.9:99–103 (1994). [CrossRef]
  31. F. Bevilacqua and C. Depeursinge, “Monte Carlo study of diffuse reflectance at source–detector separations close to one transport mean free path,” J. Opt. Soc. Am. A16:2935–2945 (1999). [CrossRef]
  32. A. Kienle, F. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett.26:1571–1573 (2001). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited