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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 5 — May. 1, 2011
  • pp: 1082–1096
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Spectral-profile-based algorithm for hemoglobin oxygen saturation determination from diffuse reflectance spectra

Po-Ching Chen and Wei-Chiang Lin  »View Author Affiliations


Biomedical Optics Express, Vol. 2, Issue 5, pp. 1082-1096 (2011)
http://dx.doi.org/10.1364/BOE.2.001082


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Abstract

Variations of hemoglobin (Hb) oxygenation in tissue provide important indications concerning the physiological conditions of tissue, and the data related to these variations are of intense interest in medical research as well as in clinical care. In this study, we derived a new algorithm to estimate Hb oxygenation from diffuse reflectance spectra. The algorithm was developed based on the unique spectral profile differences between the extinction coefficient spectra of oxy-Hb and deoxy-Hb within the visible wavelength region. Using differential wavelet transformation, these differences were quantified using the locations of certain spectral features, and, then, they were related to the oxygenation saturation level of Hb. The applicability of the algorithm was evaluated using a set of diffuse reflectance spectra produced by a Monte Carlo simulation model of photon migration and by tissue phantoms experimentally. The algorithm was further applied to the diffuse reflectance spectra acquired from in vivo experiments to demonstrate its clinical utility. The validation and evaluation results concluded that the algorithm is applicable to various tissue types (i.e., scattering properties) and can be easily used in conjunction with a diverse range of probe geometries for real-time monitoring of Hb oxygenation.

© 2011 OSA

1. Introduction

The microcirculation is that part of the vascular tree that comprises blood vessels smaller than 100 μm in diameter, including arterioles, capillaries, and venules. One of its primary roles is to distribute oxygen throughout tissues. The main oxygen carrier within the circulatory system is red blood cells (RBCs), and the oxygen transport rate in various organs is controlled by microvascular geometry, hemodynamics, and RBC hemoglobin (Hb) oxygen saturation. Since diseases and injuries can lead to certain local modifications in microvasculature, and hence microvascular oxygen transport, local tissue may be hypoxic despite normal global Hb oxygenation. For example, sepsis leads to the termination of flow in a significant number of capillaries, such that the microcirculation fails to compensate for decreased functional capillary density [1

1. R. M. Bateman, M. D. Sharpe, and C. G. Ellis, “Bench-to-bedside review: microvascular dysfunction in sepsis--hemodynamics, oxygen transport, and nitric oxide,” Crit. Care 7(5), 359–373 (2003). [CrossRef] [PubMed]

]. This change elevates the likelihood of local organ failure. Furthermore, the steady state level of Hb oxygenation in the microcirculation represents the balance between cellular O2 consumption and the supply of oxygenated blood. This, in turn, provides indirect access to the metabolic characteristics of local tissue, an important physiological indicator of tissue viability. Therefore, understanding and assessing Hb oxygenation in the microcirculation provides valuable insights into a given patient’s level of health. It is not surprising, then, that local Hb oxygenation is highly-sought information in medical research, as well as in clinical care [2

2. M. Siegemund, J. van Bommel, and C. Ince, “Assessment of regional tissue oxygenation,” Intensive Care Med. 25(10), 1044–1060 (1999). [CrossRef] [PubMed]

7

7. H. W. Wang, J. K. Jiang, C. H. Lin, J. K. Lin, G. J. Huang, and J. S. Yu, “Diffuse reflectance spectroscopy detects increased hemoglobin concentration and decreased oxygenation during colon carcinogenesis from normal to malignant tumors,” Opt. Express 17(4), 2805–2817 (2009). [CrossRef] [PubMed]

].

Common in vitro Hb oxygenation sensors can be divided into two categories: electrochemical sensors and optical sensors. In the field of medicine, the optical sensors often are selected because of their non-destructive and/or non-invasive nature. The optical sensors utilize the oxygenation-dependent absorption properties of Hb to quantify its oxygenation. Depending upon its implementation, transmitted light at two or more wavelengths will be captured. When the assumptions of constant Hb concentration and optical pathlength are valid, a simple Beer-Lambert law may be used to convert light attenuation to the relative absorption properties of Hb and, hence, Hb oxygenation. A conventional CO-oximeter is typical of such an approach [8

8. L. J. Brown, “A new instrument for the simultaneous measurement of total hemoglobin, % oxyhemoglobin, % carboxyhemoglobin, % methemoglobin, and oxygen content in whole blood,” IEEE Trans. Biomed. Eng. BME-27(3), 132–138 (1980). [CrossRef] [PubMed]

].

Accurately measuring Hb oxygenation from in vivo tissue is a difficult task because biological tissues are highly scattering. In addition, diffusely reflected light signals (i.e., diffuse reflectance spectroscopy) often are measured because of several limitations imposed by tissue geometry and measurement environment. These two conditions, collectively, complicate the process of assessing in vivo Hb oxygenation; scattering-induced light attenuation and pathlength alteration have to be considered by the photon migration model that converts diffuse reflectance signals to optical properties and then to Hb oxygenation. Several groups have modified Beer-Lambert law either empirically or theoretically to accommodate those scattering induced effects [9

9. W. T. Knoefel, N. Kollias, D. W. Rattner, N. S. Nishioka, and A. L. Warshaw, “Reflectance spectroscopy of pancreatic microcirculation,” J. Appl. Physiol. 80(1), 116–123 (1996). [PubMed]

,10

10. J. Gade, D. Palmqvist, P. Plomgård, and G. Greisen, “Diffuse reflectance spectrophotometry with visible light: comparison of four different methods in a tissue phantom,” Phys. Med. Biol. 51(1), 121–136 (2006). [CrossRef] [PubMed]

]. The more sophisticated models have been proposed, including the diffuse approximation model [11

11. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]

], the Monte Carlo (MC) based inverse model [12

12. G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45(5), 1062–1071 (2006). [CrossRef] [PubMed]

], the optical pathlength estimation model [13

13. A. A. Stratonnikov and V. B. Loschenov, “Evaluation of blood oxygen saturation in vivo from diffuse reflectance spectra,” J. Biomed. Opt. 6(4), 457–467 (2001). [CrossRef] [PubMed]

,14

14. S. L. Jacques, R. Samatham, and N. Choudhury, “Rapid spectral analysis for spectral imaging,” Biomed. Opt. Express 1(1), 157–164 (2010). [CrossRef] [PubMed]

], and the empirical model [15

15. P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10(3), 034018 (2005). [CrossRef] [PubMed]

,16

16. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46(29), 7317–7328 (2007). [CrossRef] [PubMed]

]. Within these models, a set of coefficients is used to define a diffuse reflectance spectrum, and these coefficients are adjusted systematically until the model-predicted diffuse reflectance spectrum closely resembles the one actually measured. From the optimal coefficients, the absorption properties of the measured subject can be estimated and its Hb oxygenation determined.

In this article, we propose a new algorithm that estimates Hb oxygenation by analyzing the Hb oxygenation-induced spectral profile alterations in diffuse reflectance spectra within the visible wavelength region. The algorithm utilizes the differential wavelet transform (DWT) to enhance the tracking of the spectral profile alterations and to reduce and monitor noises in the spectra at the same time. The validation and evaluation using MC simulation and tissue phantoms concluded that the algorithm is applicable to various tissue types (i.e., scattering properties) and can be easily used in conjunction with a diverse range of probe geometries for real-time monitoring of Hb oxygenation without adjustment.

2. Methods and theory

The Hb oxygenation extraction algorithm proposed in this study was developed based on an important absorption characteristic of Hb: the profile of the extinction coefficient spectrum of Hb from 450 nm to 600 nm alters drastically between the oxygenated and the deoxygenated states. The extinction coefficient spectrum of Hb at a given oxygen saturation (SatO2) level can be calculated using Eq. (1).

εSatO2(λ)=SatO2εoxy(λ)+(1SatO2)εdeoxy(λ)[liter/mole/cm],
(1)

where λ is wavelength [nm], εoxy(λ)is the extinction coefficient spectrum of oxy-Hb [liter/mole/cm], and εdeoxy(λ)is the extinction coefficient spectrum of deoxy-Hb [liter/mole/cm]. When comparing εSatO2(λ) at various SatO2 levels, it clearly shows that SatO2 level influences both the spectral feature types (e.g., peaks and valleys) as well as their locations in εSatO2(λ). Therefore SatO2 information may be extracted from εSatO2(λ) by quantifying the location of a specific spectral feature in εSatO2(λ), which is the central theorem of the proposed Hb oxygenation extraction algorithm.

To facilitate the identification and localization of a specific spectral feature in εSatO2(λ), a DWT technique was employed in the Hb oxygenation extraction algorithm. DWT of εSatO2(λ) is denoted by WsnεSatO2(u) where u is a translation, s is a scale parameter, and n is a differential parameter. From a signal processing point of view, the wavelet transform resembles a windowed band-pass filter with a passing band, its center frequency and a window spread controlled by s. Moreover, the wavelet transform also can detect and measure variations in the input signal in the area surrounding u whose size is proportional to s. The detailed definition and explanation of DWT can be found in Appendix. In the algorithm, DWT removes those unwanted frequency components from the input signal (i.e., processed signal) and various n values were used in DWT to identify different spectral feature types in εSatO2(λ); zero-crossing points of WsnεSatO2(u), denoted by Zj,s,nε, were used to localize these features [17

17. S. Mallat, “Zero-crossings of a wavelet transform,” IEEE Trans. Inf. Theory 37(4), 1019–1033 (1991). [CrossRef]

]. Specifically, Zj,s,n=1ε locates the j-th local maximum or minimum in filtered εSatO2(λ); Zj,s,n=2ε locates the j-th inflection point; Zj,s,n=3ε locates the j-th local maximum curvature.

SatO2=Sj,s,n(Zj,s,nε)[%].
(2)

In order to apply the relationship derived in Eq. (2) to diffuse reflectance spectra, preprocessing of diffuse reflectance spectra is necessary. According to the theory of photon migration, absorption events reduce the weight of a photon package during the migration process. Therefore, the remaining energy of a diffusely reflected photon package may be described as:

E(r,λ)=E0(r0,λ)eμa(λ)l(r,λ)[J],
(3)

where r is the distance between the source and detector [cm], E 0 is the initial energy of the photon package [J], r 0 is the entrance point of the photon package (i.e., source location), E(r,λ)is the remaining energy of the photon package [J] when it remerges at r, μa(λ) is the absorption coefficient of the medium [1/cm], and l(r,λ) is the migration pathlength of the photon package [cm]. Note that l(r,λ) is a function of the reduced scattering properties of the medium μs'(λ) [1/cm] as well as r [18

18. E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008). [CrossRef] [PubMed]

]. A steady-state diffuse reflectance signal Rd(r,λ) [W], therefore, is the sum of the all escaped photons at a given surface location per unit time. That is,

Rd(r,λ)=i=1xEi(r,λ)T=E0(r,λ)Ti=1xeμa(λ)li(r,λ)E0(r,λ)Teμa(λ)k(r,λ)[W],
(4)

where x is the number of diffusely reflected photon packages remerged at r and it is a probability determined by μs'(λ) and r, T is the time to deliver the entire incident photon packages, and k(r,λ) is a constant calculated from k(r,λ)=ln(i=1xeμa(λ)l(r,λ))/μa(λ). Based on this theory, a natural logarithmic operation could be applied to Rd(r,λ) to obtain the absorption characteristics (i.e., μa(λ)) and the scattering characteristics (i.e., k(r,λ)). Assuming Hb is the only dominant chromophore of biological tissues between 450 nm and 600 nm and the spectral profile of k(r,λ) is relatively monotonic, the spectral profile of ln[Rd(r,λ)] between 450 nm and 600 nm should strongly resemble that of εSatO2(λ)within the same spectral region.

To effectively detect the spectral profile alterations in ln[Rd(r,λ)] induced by SatO2 variations, DWT was again used on ln[Rd(r,λ)]. The transformed ln[Rd(r,λ)] is denoted by Wsn{ln[Rd(r,u)]}. The locations of the spectral features in ln[Rd(r,λ)] are tracked by the zero-crossing points in Wsn{ln[Rd(r,u)]}, which are denoted by Zj,s,nRd. In the extraction algorithm, it is assumed that Zj,s,nε acquired from the extinction spectra should be coincided with Zj,s,nRd. Therefore, Sj,s,n in Eq. (2) can be used as the lookup functions to estimate the SatO2 level in Rd(r,λ) using Zj,s,nRd as the inputs. That is,

SatO2(j,s,n)est=Sj,s,n(Zj,s,nRd)[%]
(5)

3. Algorithm validation and evaluation using Monte Carlo simulation

To validate the proposed algorithm, an extensive diffuse reflectance spectra database was created using a MC simulation model of photon migration. In the simulation model, a semi-infinite medium with homogenous optical properties was used to mimic a biological tissue. In each simulation, a total of three million photons were injected into the medium at the origin (i.e., (r,z) = (0,0)). The energy of reflected photons was recorded as a function of the exit position r in order to create the diffuse reflectance spectra Rdsim(r,λ).

Within the spectral region of 400 nm to 650 nm, Hb is the dominant chromophore in biological tissues and processes unique spectral profile characteristics. In contrast, other biological chromophores do not have distinct spectral features in the same wavelength region. In the MC simulation model, the only absorber used was Hb. The absorption property of the simulated medium hence was defined by the following equation:

μa(λ)=BVF[SatO2¯×μaoxy(λ)+(1SatO2¯)×μadeoxy(λ)][1/cm],
(6)

where BVF is the blood volume fraction, SatO2¯ is the user-defined SatO2 level of Hb [%], μaoxy(λ) is the absorption coefficient of oxygenated blood [1/cm], and μadeoxy(λ)is the absorption coefficient of deoxygenated blood [1/cm]. μaoxy(λ)and μadeoxy(λ) were obtained from εoxy(λ)and εdeoxy(λ), respectively, with the whole blood Hb concentration of 150 gram/liter. The reduced scattering coefficients in biological tissue were approximated by the following equation [11

11. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]

,19

19. A. M. Nilsson, C. Sturesson, D. L. Liu, and S. Andersson-Engels, “Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy,” Appl. Opt. 37(7), 1256–1267 (1998). [CrossRef] [PubMed]

]. That is,

μs'(λ)=A×wB[1/cm],
(7)

where w=λ×103. The ranges of all variables associated with the optical properties are summarized in Table 1

Table 1. Variables used in constructing Rdsim(r,λ) and their ranges used

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. Note that the ranges of the optical properties used to construct Rdsim(r,λ) encompass the majority of biological tissue types and hemodynamic conditions. Furthermore, Rdsim(r,λ) was recorded from r = 0.0075 cm to r = 0.9975 cm, which covers the source-detection separations commonly used in the in vivo diffuse reflectance spectroscopy studies.

SatO2(j,s,n)error=|SatO2¯SatO2(j,s,n)est|[%],
(8)

where SatO2¯ is the actual SatO2 level of the Hb used in the MC simulations, as defined in Eq. (6), and SatO2(j,s,n)est is the estimated SatO2 level of Hb derived from the extraction algorithm using Eq. (5). SatO2(j,s,n)error was calculated with extended combinations of (j,s,n). The Sj,s,n, as defined in Eq. (5), producing the lowest mean SatO2(j,s,n)error over the entire range of the simulation parameters was identified as the ideal lookup function to retrieve the SatO2 level of Hb from a diffuse reflectance spectrum using the proposed algorithm.

4. Algorithm validation and evaluation using tissue phantoms and in vivo experiments

To demonstrate its clinical utility, the proposed Hb oxygenation extraction algorithm was applied to the diffuse reflectance spectra acquired from tissue phantoms and in vivo tissue, using a fiber-optic spectroscopy system. The system utilized a tungsten-halogen lamp (LS-1, Ocean Optics, Dunedin, FL) as the excitation source and a spectrometer (USB 2000, Ocean Optics, Dunedin, FL) to record diffuse reflectance spectra. A fiber-optic probe was employed for excitation light delivery and reflected light collection. All the experimentally-acquired diffuse reflectance spectra were calibrated against a standard (FGS-20-02c, Avian Technologies, NH), so as to remove the spectral profile alterations induced by the spectroscopy system, and then re-sampled to reduce the spectral data interval to 2 nm.

The tissue phantoms used in the experiments consisted of a mixture of whole blood and scatterers in a saline solution. The blood samples were heparinized after their acquisition from healthy human subjects. The scatterers added to the solution were 1μm microspheres (Polysciences Inc., Warrington, PA). Two tissue phantoms were prepared for the experiments. The BVF of whole blood samples were 0.05 in Phantom 1 and 0.03 in Phantom 2. The concentrations of the scatters were 0.0159 particle/μm3 in Phantom 1 and 0.0108 particle/μm3 in Phantom 2. According to Mei theory estimates, the scattering properties resulting from the added scatterers were 31.7 1/cm at 500nm and 29.0 1/cm at 600nm for Phantom 1; and 21.5 1/cm at 500nm and 19.7 1/cm at 600nm for Phantom 2. The SatO2 level of Hb in the phantom was first elevated by bubbling oxygen into the phantom. Then the phantom was deoxygenated by bubbling nitrogen into it. During the de-oxygenation process, the SatO2 level of the Hb was estimated by applying the proposed algorithm to the diffuse reflectance signals acquired from the phantom surface using a fiber-optic diffuse reflectance spectroscopy system. In the probe, two identical fibers, each having a 200μm core-diameter were used, one for excitation and the other for detection, and the source-detector separation distance of the probe was 1652μm. Meanwhile, a small amount of the tissue phantom was extracted and placed into a separate apparatus to measure its collimated transmission, Tc(λ). The same measurement also was carried out with a reference sample containing the same concentration of scatterers, but no whole blood, to yield Tc,ref(λ). From the ratio of Tc(λ) to Tc,ref(λ), the absorption properties of the phantom sample μa,phantom(λ) were determined using modified Beer’s law. Sequentially, the SatO2 level of Hb in the phantom sample (SatO2,ref) was derived from μa,phantom(λ) using the Hb extinction coefficient fitting routine. Please note that the fitting routine was applied to μa,phantom(λ) between 650 nm to 850 nm, in order to avoid the effect of Hb packing in red blood cells [20

20. J. C. Finlay and T. H. Foster, “Effect of pigment packaging on diffuse reflectance spectroscopy of samples containing red blood cells,” Opt. Lett. 29(9), 965–967 (2004). [CrossRef] [PubMed]

].

In the first in vivo experiment, the algorithm was used to extract the local Hb oxygenation information at a fingertip under normal and ischemic conditions. The fiber-optic probe used in this experiment consisted of three 600 μm core-diameter optical fibers: one was used for excitation and the other two (fiber A and fiber B) for detection. The distances between the center of the excitation fiber and those of the detection fibers were 810 μm for fiber A and 1116 μm for fiber B. During the experiment, the probe was placed in direct contact with the fingertip, using a probe holder, to maintain stability of the contact position and pressure. Two spectrometers were used to acquire the diffuse reflectance spectra from the two detection fibers separately and simultaneously. A short-term local ischemic condition of the fingertip was created by tightening a rubber band placed at the base of the finger to reduce blood flow for 400 seconds. Diffuse reflectance spectra were acquired continuously at the rate of 0.5 Hz prior to the occlusion to establish a normal reference, during the ischemia and after releasing the rubber band.

5. Spectral signal quality evaluation

MC simulation is a statistical-based model and requires a large number of repetitions (i.e., input photons) to reduce the noises. Diffuse reflectance spectra acquired by both in vivo experiments and MC simulation inevitably contain noises. For this reason, the noise level of ln[Rd(r,λ)] and its impacts on the performance of the Hb oxygenation extraction algorithm were evaluated. To accomplish this goal, the signal to noise ratios (S/N) of ln[Rd(r,λ)] had to be defined first. As mentioned previously, DWT is capable of filtering. With s = 1, DWT of ln[Rd(r,λ)] isolates the highest frequency component in ln[Rd(r,λ)], which is treated as the noise component. Therefore, depending on the s and n parameters used in DWT, S/N of a transformed ln[Rd(r,λ)] with s > 1 can be conveniently estimated using the following equation:

S/N(s,n)=|u=540560Wsn{ln[Rd(r,u)]}|2|u=540560W1n{ln[Rd(r,u)]}|2.
(9)

6. Results

According to Table 1, the database of Rdsim(r,λ) consists of 350240 spectra. During the evaluation and the validation, however, some spectra, especially those with large source-detector separations r, were considered as unusable because they contained zero data points (i.e., no signal). The average S/N of transformed Rdsim(r,λ) at each r was used to evaluate this phenomenon. It was found that the number of unusable spectra increases and the S/N of transformed spectra decreases when r exceeds 0.3 cm. Figure 1
Fig. 1 The correlation between the number of unusable spectra and S/N(s,n) at various r. The long dash line represents the number of unusable spectra in Rdsim(r,λ). The solid curve is the mean S/N of transformedRdsim(r,λ), and the error bars represent the standard deviations. Panel (a) represents the condition of s = 6 and n = 2 in DWT. Panel (b) represents the condition of s = 6 and n = 3 in DWT
demonstrates two examples of the average S/N versus number of unusable spectra at various r with different s and n combinations. In order to avoid the errors induced by poor S/N over the majority optical property ranges defined in Table 1, the following evaluation and validation were carried out for r ≤ 0.3 cm only. This limitation results in a total of 103840 spectra, 9440 spectra per SatO2 level, and 1760 at each r in the reduced Rdsim(r,λ) database.

Upon identifying the two ideal lookup functions, their corresponding estimation errors, namely SatO2(2,6,2)error and SatO2(4,6,3)error, were used to evaluate the performance of the proposed Hb oxygenation extraction algorithm. The overall estimation error of the algorithm is 1.23% ± 1.35% (mean ± standard deviation) for the entire reduced Rdsim(r,λ) database.

Influences of individual variable defined in Table 1 on the performance of the algorithm also were individually evaluated. The analysis was carried out by calculating the estimation errors at all levels of one given variable, while the remaining variables were adjusted over the entire ranges.

The estimation errors at various SatO2 levels are shown in Fig. 4 (a)
Fig. 4 (a) SatO2 –dependence and (b) BVF-dependence of the SatO2 estimation errors. The solid bars represent the average estimation errors; the error bars represent the one standard deviation.
. The results indicate that the estimation errors are the highest at the SatO2 level of 30%. This level is the transition point at which one lookup function is replaced by the other one to interpret the SatO2 level. The accuracy of the algorithm was also evaluated as a function of BVF, and the results are shown in Fig. 4 (b). In general, the SatO2 estimation errors do not change significantly in accordance with the variations in BVF. The estimation error increases as the BVF level decreases; the highest estimation error (1.7%) is found at BVF = 0.01.

The SatO2 estimation errors were evaluated in according with the parameters A and B, which are used to define the reduced scattering coefficientμs'(λ) in Eq. (7). The outcomes, as shown in Fig. 5
Fig. 5 μs'(λ)-dependence of the SatO2 estimation errors. The solid bars represent the average estimation errors; the error bars represent the one standard deviation.
, again suggest that the estimation errors are constant for all μs'(λ) levels.

As mentioned previously, the decision of choosing the ideal lookup functions and the evaluation of the algorithm were determined using the reduced Rdsim(r,λ) database (r < 0.3 cm). When applying this algorithm to the entire Rdsim(r,λ) database (i.e., r = 0.0075 cm to r = 0.9975 cm), the overall estimation error of the algorithm increases to 2.39% ± 3.64%. Figure 6
Fig. 6 r-dependence of the SatO2 estimation errors. The solid line represents the average estimation errors; the error bars represent the one standard deviation. The long dash line represents the number of usable spectra in Rdsim(r,λ).
illustrates the estimation errors as a function of r, derived from the entire Rdsim(r,λ) database. As mentioned before, the number of usable spectra drops when r exceeds 0.3 cm. The estimation errors increase when r approaches the two extremes and the lowest estimation error was found between r = 0.06 cm to r = 0.15 cm.

Through the observations described above, it was found that the average estimation errors tend to increase when the mean S/N declines. To illustrate this negative correlation, the estimation errors were plotted against S/N(2,6,2) for SatO2 ≥ 40% and S/N(4,6,3) for SatO2 < 40% respectively in Fig. 7
Fig. 7 The relationship between the estimation errors versus S/N(2,6,2) for SatO2 ≥ 40% and S/N(4,6,3) for SatO2 < 40%. The solid bars represent the average estimation errors within a specific range of S/N; the error bars represent the one standard deviation. The solid line represents the overall estimation error (2.39%).
. Figure 7 also reveals that the average estimation errors rise above the overall estimation error when S/N(2,6,2) for SatO2 ≥ 40% and S/N(4,6,3) for SatO2 < 40% descend below 700 and 70, respectively.

The results of tissue phantom experiments are plotted in Fig. 8(a)
Fig. 8 (a) Results of the tissue phantom study. Each symbol represents the SatO2 level estimated by the algorithm and the SatO2,ref level determined by collimated transmission during the de-oxygenation process of two tissue phantoms. The line indicates unity. (b) Time histories of local SatO2 variations at the fingertip during experimentally-induced ischemia. The SatO2 levels were derived from the diffuse reflectance spectra, recorded through fiber A and fiber B, using the proposed algorithm.
, which depicts very good agreement between the SatO2 levels estimated by the proposed algorithm and the SatO2,ref (reference) levels for both tissue phantoms employed. The Pearson correlation coefficient between the two variables was 0.99, with p < 0.05. Using SatO2,ref as the error-free standard, the average estimation error of the algorithm was calculated as 2.4% ± 2.4% (n = 20) for Phantom 1 and 2.3% ± 2.5% (n = 22) for Phantom 2.

For the in vivo fingertip ischemia experiment, the spectral data were taken from the tip of the middle finger of a volunteer (P. C.): the results are shown in Fig. 8 (b). The proximity of the two curves indicates that the SatO2 levels extracted using the diffuse reflectance spectra from the two detection fibers are fairly similar. For the first 400 seconds (normal reference), the average SatO2 level of the fingertip was 68.45% ± 2.55% from fiber A and 70.49% ± 2.55% from fiber B. The SatO2 level started to decline right after the rubber band was tightened and eventually plateaued. During the steady-state ischemic condition (i.e., 600 sec to 800 sec), the average SatO2 levels from fiber A and fiber B were 16.77% ± 2.90% and 17.01% ± 1.87%, respectively. The mean difference between fibers A and B was reduced during this period, relative to the normal reference level. The SatO2 level returned to normal range, as expected, once the rubber band was released.

The demographic and histological information of the six brain tumor patients who participated in the clinical study are provided in Table 2

Table 2. Demographic data on the 6 patients who participated in the clinical study

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. Figure 9
Fig. 9 Representative time histories of the estimated SatO2 levels of normal cortex (black) and tumor (grey) from all six patients.
represents the estimated SatO2 level by the algorithm for each patient in normal cortex and the tumor area within the 12 second acquisition period. Figure 9 illustrates how the SatO2 level may fluctuate during acquisition. However, in general, normal cortex exhibited relatively higher SatO2 levels than tumor areas within the same patient. The average SatO2 level of the six patients was 66.42% ± 8.86% within normal cortex and 50.89% ± 13.09% in brain tumor. The S/N of all the experimental spectra were evaluated using Eq. (9) and found above the threshold depicted in Fig. 7.

7. Discussion and conclusion

MC simulation for photon migration has become a standard for predicting photon migration in biological tissues [22

22. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE, Bellingham, 2007).

]. One critical advantage of the MC model is that it can be used to evaluate a broad range of tissue optical characteristics efficiently. While constructing the Rdsim(r,λ) database for the algorithm validation, the ranges of the optical properties selected encompass the majority of in vivo biomedical tissues. The outcome of validation shows that the algorithm provides satisfactory accuracy for r is less than 0.3 cm. Furthermore, the estimation performance of the algorithm is fairly constant over the entire optical property range, as indicated by low and even estimation errors. This demonstrates the applicability of the algorithm to extract the SatO2 level of Hb from diffuse reflectance spectra measured for various tissue types in vivo.

The tissue phantom experiment was performed to further ascertain the validity of the algorithm. The algorithm exhibits adequate estimation accuracy versus SatO2,ref in both tissue phantoms with different BVF and scattering properties. This finding further supports the validation and evaluation outcomes using simulated spectra generated by the MC simulation. As mentioned previously, a whole blood sample was used in the tissue phantom study and a packing effect of Hb in red blood cells (i.e., inhomogeneity in Hb distribution) was evident. According to Finlay et al. [20

20. J. C. Finlay and T. H. Foster, “Effect of pigment packaging on diffuse reflectance spectroscopy of samples containing red blood cells,” Opt. Lett. 29(9), 965–967 (2004). [CrossRef] [PubMed]

], the packing effect has a relatively small influence on the visible absorption peaks and can be ignored in the near-infrared region. SatO2,ref was calculated from μa,phantom(λ) in the wavelength region of 650 to 850nm. The phantom study demonstrated that the SatO2 levels of Hb estimated by our algorithm closely match SatO2,ref levels. This suggests that the packing effect has little impact on our algorithm.

Through the derivation and validation processes, several advantages of the proposed algorithm were noticed. The operation of the algorithm involves conducting two transformations to the input (i.e., Rd(r,λ)) and applying the target spectral feature location (i.e., Zj,s,nRd) to its corresponding lookup function Sj,s,n. This process is much simpler than the repeated fitting routine (i.e., inverse approach) required by many other models [11

11. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]

16

16. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46(29), 7317–7328 (2007). [CrossRef] [PubMed]

]. The computational resources required by the proposed algorithm are minimal, which makes it suitable for real-time applications. Furthermore, with an appropriate selection of the spectral profile features and hence the lookup functions, the algorithm is insensitive to the scattering properties and BVF of the biological media, as well as to the source-to-detector separation. In other words, the proposed Hb extraction algorithm with a set of established lookup functions can be immediately applied to the in vivo diffuse reflectance spectra acquired from various tissue types using optical probes with a wide range of source-detection geometry without adjustment.

The utilization of DWT in the proposed extraction algorithm also reduces the impact of spectral noise on the accuracy of the SatO2 level assessment. As mentioned before, the DWT process is capable of signal filtering; unwanted noise in the signal is removed by a tunable linear band-pass filter. In addition, the noise level in signals can be assessed by DWT with a small scale, which provides a convenient way to access the quality of the signals (i.e., S/N) instantaneously and further ensure the accuracy of the estimation. In terms of S/N, we believe the S/N level of the signal, as defined by (9), should be higher than 700 and 70 for S2,6,2 and S4,6,3, respectively, in order to achieve acceptable algorithm accuracy. This conclusion is derived based upon the S/N-estimation error analysis shown in Fig. 7. It is found that the information regarding how signal quality affects the performance of other reported models is insufficient.

All other models citied in the Introduction section access SatO2 level of Hb by relying on identifying the absorption properties of the tissue, which needs to take the excitation intensity of the light source into consideration. To adapt the experimental diffuse reflectance to different models, various intensity calibration procedures need to be employed for each method. Some methods calculate the attenuation/optical density spectrum by using a reference spectrum acquired from an intensity-dependent reference sample [9

9. W. T. Knoefel, N. Kollias, D. W. Rattner, N. S. Nishioka, and A. L. Warshaw, “Reflectance spectroscopy of pancreatic microcirculation,” J. Appl. Physiol. 80(1), 116–123 (1996). [PubMed]

,10

10. J. Gade, D. Palmqvist, P. Plomgård, and G. Greisen, “Diffuse reflectance spectrophotometry with visible light: comparison of four different methods in a tissue phantom,” Phys. Med. Biol. 51(1), 121–136 (2006). [CrossRef] [PubMed]

,13

13. A. A. Stratonnikov and V. B. Loschenov, “Evaluation of blood oxygen saturation in vivo from diffuse reflectance spectra,” J. Biomed. Opt. 6(4), 457–467 (2001). [CrossRef] [PubMed]

]. Other methods calibrate their diffuse reflectance spectrum intensities directly to the measurements acquired from one or multiple phantoms with known optical properties [12

12. G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45(5), 1062–1071 (2006). [CrossRef] [PubMed]

,15

15. P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10(3), 034018 (2005). [CrossRef] [PubMed]

,16

16. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46(29), 7317–7328 (2007). [CrossRef] [PubMed]

]. And still other models avoid this calibration procedure by introducing an intensity coupling/proportionality factor into their fitting routines [11

11. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]

,14

14. S. L. Jacques, R. Samatham, and N. Choudhury, “Rapid spectral analysis for spectral imaging,” Biomed. Opt. Express 1(1), 157–164 (2010). [CrossRef] [PubMed]

]. The algorithm that we propose uses the spectral profile features in a diffuse reflectance spectrum to determine its corresponding SatO2 level of Hb. Hence, knowing the absolute intensity of the light source is not needed. In other words, only simple calibration to the diffuse reflectance spectroscopy system is required to remove all possible spectral profile alterations induced by the instrumentation itself.

To ensure the accuracy of the extraction algorithm, the spectral profile characteristics of the input signals (i.e., Rd(r,λ)) must be well preserved. In other words, the success of applying the algorithm hinges upon the spectral resolution. During the development and evaluation processes, a 2 nm spectral resolution was used in both εSatO2(λ) and Rdsim(r,λ). This spectral resolution is easily achievable with the spectrometers in today’s market. Further investigation is required to elucidate the impact of lower spectral resolution on the accuracy of the extraction algorithm.

The extraction algorithm operates within the spectral region, 450 nm to 600 nm, where the Hb absorption spectrum is rich in spectral profile features. Unfortunately, this is also the region where the Hb absorption is very strong. This characteristic impedes the photons from penetrating deeply into tissue. According to the results generated using the MC simulations, the penetration depth of light within this region usually falls within one or two millimeters, depending on the tissue type and the Hb concentration in the tissue. In addition, the high absorption characteristics of Hb in this spectral region also limits the source-detector separation to preserve the S/N of the signals. These two factors, together, limit the volume of tissue investigated by the diffuse reflectance spectroscopy system employing the extraction algorithm for SatO2 assessment. Under this circumstance, the suitable instrumentation partners for the algorithm would be systems with fiber-optic based setups that acquire diffuse reflectance from tissues using surface probes, catheters or needles. Such a combination will be ideal for studies of in vivo microcirculation for which focal information is required.

8. Appendix A

The continuous wavelet transformation of εSatO2(λ)is defined by

WsεSatO2(u)=+εSatO2(λ)1sψ(λus)dλ,
(A1)

where ψ(λ) is the mother wavelet and s is the scaling parameter and u is the translation parameter. Equation (A1) can be rewritten into a convolution format as

WsεSatO2(u)=f×ψs(u),
(A2)

where ψs(λ)=1/sψ(λ/s) and × denotes convolution. The wavelet needs to have a zero average ψ(λ)dλ=0 and the Fourier transform of ψs(λ) is ψ^s(ω)=sψ^(sω). This indicates that the wavelet transform processes the input single in a fashion similar to a tunable band-pass filter [27

27. S. Mallat, A Wavelet Tour of Signal Processing (Academic, London, 1999).

].

If the wavelet function has n vanishing moments and it can be rewritten as nth derivative of a function [27

27. S. Mallat, A Wavelet Tour of Signal Processing (Academic, London, 1999).

]. That is ψ(λ)=(1)ndnρ(λ)/dλn. The wavelet transformation can be rewritten into a format of differential wavelet transform defined as

WsnεSatO2(u)=sndndun(εSatO2×ρs)(u),
(A3)

where ρs(λ)=1/sρ(λ/s). In this application, a Gaussian smoothing function is chosen for ρ(λ).

Acknowledgments

The authors would like to thank Dr. Dulikravich of the Department of Mechanical and Materials Engineering at Florida International University, who granted the authors the access to the Tesla-128 computer cluster, which helped the authors complete the MC database. The financial supporters of the project include the American Heart Association (0655392B), the Thrasher Research Fund, the Ware Foundation Research Endowment, and Florida International University Dissertation Year Fellowship.

References and links

1.

R. M. Bateman, M. D. Sharpe, and C. G. Ellis, “Bench-to-bedside review: microvascular dysfunction in sepsis--hemodynamics, oxygen transport, and nitric oxide,” Crit. Care 7(5), 359–373 (2003). [CrossRef] [PubMed]

2.

M. Siegemund, J. van Bommel, and C. Ince, “Assessment of regional tissue oxygenation,” Intensive Care Med. 25(10), 1044–1060 (1999). [CrossRef] [PubMed]

3.

D. A. Benaron, I. H. Parachikov, S. Friedland, R. Soetikno, J. Brock-Utne, P. J. van der Starre, C. Nezhat, M. K. Terris, P. G. Maxim, J. J. Carson, M. K. Razavi, H. B. Gladstone, E. F. Fincher, C. P. Hsu, F. L. Clark, W. F. Cheong, J. L. Duckworth, and D. K. Stevenson, “Continuous, noninvasive, and localized microvascular tissue oximetry using visible light spectroscopy,” Anesthesiology 100(6), 1469–1475 (2004). [CrossRef] [PubMed]

4.

C. Verdant and D. De Backer, “How monitoring of the microcirculation may help us at the bedside,” Curr. Opin. Crit. Care 11(3), 240–244 (2005). [CrossRef] [PubMed]

5.

H. Knotzer and W. R. Hasibeder, “Microcirculatory function monitoring at the bedside--a view from the intensive care,” Physiol. Meas. 28(9), R65–R86 (2007). [CrossRef] [PubMed]

6.

R. Mallia, S. S. Thomas, A. Mathews, R. Kumar, P. Sebastian, J. Madhavan, and N. Subhash, “Oxygenated hemoglobin diffuse reflectance ratio for in vivo detection of oral pre-cancer,” J. Biomed. Opt. 13(4), 041306 (2008). [CrossRef] [PubMed]

7.

H. W. Wang, J. K. Jiang, C. H. Lin, J. K. Lin, G. J. Huang, and J. S. Yu, “Diffuse reflectance spectroscopy detects increased hemoglobin concentration and decreased oxygenation during colon carcinogenesis from normal to malignant tumors,” Opt. Express 17(4), 2805–2817 (2009). [CrossRef] [PubMed]

8.

L. J. Brown, “A new instrument for the simultaneous measurement of total hemoglobin, % oxyhemoglobin, % carboxyhemoglobin, % methemoglobin, and oxygen content in whole blood,” IEEE Trans. Biomed. Eng. BME-27(3), 132–138 (1980). [CrossRef] [PubMed]

9.

W. T. Knoefel, N. Kollias, D. W. Rattner, N. S. Nishioka, and A. L. Warshaw, “Reflectance spectroscopy of pancreatic microcirculation,” J. Appl. Physiol. 80(1), 116–123 (1996). [PubMed]

10.

J. Gade, D. Palmqvist, P. Plomgård, and G. Greisen, “Diffuse reflectance spectrophotometry with visible light: comparison of four different methods in a tissue phantom,” Phys. Med. Biol. 51(1), 121–136 (2006). [CrossRef] [PubMed]

11.

R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]

12.

G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45(5), 1062–1071 (2006). [CrossRef] [PubMed]

13.

A. A. Stratonnikov and V. B. Loschenov, “Evaluation of blood oxygen saturation in vivo from diffuse reflectance spectra,” J. Biomed. Opt. 6(4), 457–467 (2001). [CrossRef] [PubMed]

14.

S. L. Jacques, R. Samatham, and N. Choudhury, “Rapid spectral analysis for spectral imaging,” Biomed. Opt. Express 1(1), 157–164 (2010). [CrossRef] [PubMed]

15.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10(3), 034018 (2005). [CrossRef] [PubMed]

16.

R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46(29), 7317–7328 (2007). [CrossRef] [PubMed]

17.

S. Mallat, “Zero-crossings of a wavelet transform,” IEEE Trans. Inf. Theory 37(4), 1019–1033 (1991). [CrossRef]

18.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008). [CrossRef] [PubMed]

19.

A. M. Nilsson, C. Sturesson, D. L. Liu, and S. Andersson-Engels, “Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy,” Appl. Opt. 37(7), 1256–1267 (1998). [CrossRef] [PubMed]

20.

J. C. Finlay and T. H. Foster, “Effect of pigment packaging on diffuse reflectance spectroscopy of samples containing red blood cells,” Opt. Lett. 29(9), 965–967 (2004). [CrossRef] [PubMed]

21.

W. C. Lin, D. I. Sandberg, S. Bhatia, M. Johnson, S. Oh, and J. Ragheb, “Diffuse reflectance spectroscopy for in vivo pediatric brain tumor detection,” J. Biomed. Opt. 15(6), 061709 (2010). [CrossRef] [PubMed]

22.

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE, Bellingham, 2007).

23.

N. T. Evans and P. F. Naylor, “The oxygen tension gradient across human epidermis,” Respir. Physiol. 3(1), 38–42 (1967). [CrossRef] [PubMed]

24.

Y. Ti and W. C. Lin, “Effects of probe contact pressure on in vivo optical spectroscopy,” Opt. Express 16(6), 4250–4262 (2008). [CrossRef] [PubMed]

25.

B. Meyer, C. Schaller, C. Frenkel, B. Ebeling, and J. Schramm, “Distributions of local oxygen saturation and its response to changes of mean arterial blood pressure in the cerebral cortex adjacent to arteriovenous malformations,” Stroke 30(12), 2623–2630 (1999). [PubMed]

26.

R. L. Jensen, “Brain tumor hypoxia: tumorigenesis, angiogenesis, imaging, pseudoprogression, and as a therapeutic target,” J. Neurooncol. 92(3), 317–335 (2009). [CrossRef] [PubMed]

27.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, London, 1999).

OCIS Codes
(070.4790) Fourier optics and signal processing : Spectrum analysis
(170.1610) Medical optics and biotechnology : Clinical applications
(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics
(300.6550) Spectroscopy : Spectroscopy, visible

ToC Category:
Spectroscopic Diagnostics

History
Original Manuscript: January 4, 2011
Revised Manuscript: March 29, 2011
Manuscript Accepted: April 1, 2011
Published: April 5, 2011

Citation
Po-Ching Chen and Wei-Chiang Lin, "Spectral-profile-based algorithm for hemoglobin oxygen saturation determination from diffuse reflectance spectra," Biomed. Opt. Express 2, 1082-1096 (2011)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-5-1082


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References

  1. R. M. Bateman, M. D. Sharpe, and C. G. Ellis, “Bench-to-bedside review: microvascular dysfunction in sepsis--hemodynamics, oxygen transport, and nitric oxide,” Crit. Care 7(5), 359–373 (2003). [CrossRef] [PubMed]
  2. M. Siegemund, J. van Bommel, and C. Ince, “Assessment of regional tissue oxygenation,” Intensive Care Med. 25(10), 1044–1060 (1999). [CrossRef] [PubMed]
  3. D. A. Benaron, I. H. Parachikov, S. Friedland, R. Soetikno, J. Brock-Utne, P. J. van der Starre, C. Nezhat, M. K. Terris, P. G. Maxim, J. J. Carson, M. K. Razavi, H. B. Gladstone, E. F. Fincher, C. P. Hsu, F. L. Clark, W. F. Cheong, J. L. Duckworth, and D. K. Stevenson, “Continuous, noninvasive, and localized microvascular tissue oximetry using visible light spectroscopy,” Anesthesiology 100(6), 1469–1475 (2004). [CrossRef] [PubMed]
  4. C. Verdant and D. De Backer, “How monitoring of the microcirculation may help us at the bedside,” Curr. Opin. Crit. Care 11(3), 240–244 (2005). [CrossRef] [PubMed]
  5. H. Knotzer and W. R. Hasibeder, “Microcirculatory function monitoring at the bedside--a view from the intensive care,” Physiol. Meas. 28(9), R65–R86 (2007). [CrossRef] [PubMed]
  6. R. Mallia, S. S. Thomas, A. Mathews, R. Kumar, P. Sebastian, J. Madhavan, and N. Subhash, “Oxygenated hemoglobin diffuse reflectance ratio for in vivo detection of oral pre-cancer,” J. Biomed. Opt. 13(4), 041306 (2008). [CrossRef] [PubMed]
  7. H. W. Wang, J. K. Jiang, C. H. Lin, J. K. Lin, G. J. Huang, and J. S. Yu, “Diffuse reflectance spectroscopy detects increased hemoglobin concentration and decreased oxygenation during colon carcinogenesis from normal to malignant tumors,” Opt. Express 17(4), 2805–2817 (2009). [CrossRef] [PubMed]
  8. L. J. Brown, “A new instrument for the simultaneous measurement of total hemoglobin, % oxyhemoglobin, % carboxyhemoglobin, % methemoglobin, and oxygen content in whole blood,” IEEE Trans. Biomed. Eng. BME-27(3), 132–138 (1980). [CrossRef] [PubMed]
  9. W. T. Knoefel, N. Kollias, D. W. Rattner, N. S. Nishioka, and A. L. Warshaw, “Reflectance spectroscopy of pancreatic microcirculation,” J. Appl. Physiol. 80(1), 116–123 (1996). [PubMed]
  10. J. Gade, D. Palmqvist, P. Plomgård, and G. Greisen, “Diffuse reflectance spectrophotometry with visible light: comparison of four different methods in a tissue phantom,” Phys. Med. Biol. 51(1), 121–136 (2006). [CrossRef] [PubMed]
  11. R. M. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999). [CrossRef] [PubMed]
  12. G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45(5), 1062–1071 (2006). [CrossRef] [PubMed]
  13. A. A. Stratonnikov and V. B. Loschenov, “Evaluation of blood oxygen saturation in vivo from diffuse reflectance spectra,” J. Biomed. Opt. 6(4), 457–467 (2001). [CrossRef] [PubMed]
  14. S. L. Jacques, R. Samatham, and N. Choudhury, “Rapid spectral analysis for spectral imaging,” Biomed. Opt. Express 1(1), 157–164 (2010). [CrossRef] [PubMed]
  15. P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10(3), 034018 (2005). [CrossRef] [PubMed]
  16. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46(29), 7317–7328 (2007). [CrossRef] [PubMed]
  17. S. Mallat, “Zero-crossings of a wavelet transform,” IEEE Trans. Inf. Theory 37(4), 1019–1033 (1991). [CrossRef]
  18. E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008). [CrossRef] [PubMed]
  19. A. M. Nilsson, C. Sturesson, D. L. Liu, and S. Andersson-Engels, “Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy,” Appl. Opt. 37(7), 1256–1267 (1998). [CrossRef] [PubMed]
  20. J. C. Finlay and T. H. Foster, “Effect of pigment packaging on diffuse reflectance spectroscopy of samples containing red blood cells,” Opt. Lett. 29(9), 965–967 (2004). [CrossRef] [PubMed]
  21. W. C. Lin, D. I. Sandberg, S. Bhatia, M. Johnson, S. Oh, and J. Ragheb, “Diffuse reflectance spectroscopy for in vivo pediatric brain tumor detection,” J. Biomed. Opt. 15(6), 061709 (2010). [CrossRef] [PubMed]
  22. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd ed. (SPIE, Bellingham, 2007).
  23. N. T. Evans and P. F. Naylor, “The oxygen tension gradient across human epidermis,” Respir. Physiol. 3(1), 38–42 (1967). [CrossRef] [PubMed]
  24. Y. Ti and W. C. Lin, “Effects of probe contact pressure on in vivo optical spectroscopy,” Opt. Express 16(6), 4250–4262 (2008). [CrossRef] [PubMed]
  25. B. Meyer, C. Schaller, C. Frenkel, B. Ebeling, and J. Schramm, “Distributions of local oxygen saturation and its response to changes of mean arterial blood pressure in the cerebral cortex adjacent to arteriovenous malformations,” Stroke 30(12), 2623–2630 (1999). [PubMed]
  26. R. L. Jensen, “Brain tumor hypoxia: tumorigenesis, angiogenesis, imaging, pseudoprogression, and as a therapeutic target,” J. Neurooncol. 92(3), 317–335 (2009). [CrossRef] [PubMed]
  27. S. Mallat, A Wavelet Tour of Signal Processing (Academic, London, 1999).

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