A method to non-invasively and quantitatively measure muscle oxygen saturation (SmO2) using broadband continuous-wave diffuse reflectance near infrared (NIR) spectroscopy is presented. The method obtained SmO2 by first correcting NIR spectra for absorption and scattering of skin pigment and fat, then fitting to a Taylor expansion attenuation model. A non-linear least squares optimization algorithm with set boundary constraints on the fitting parameters was used to fit the model to the acquired spectra. A data preprocessing/optimization scheme for accurately determining the initial values needed for the optimization was also employed. The method was evaluated on simulated muscle spectra with 4 different scattering properties, as well as on in vivo forearm spectra from 5 healthy volunteer subjects during arterial occlusion. Measurement repeatability was assessed on 24 healthy volunteers with 5 repeated measurements, each separated by at least 48 hours.
© 2007 Optical Society of America
Since Jöbsis first described the application of near infrared (NIR) spectroscopy (NIRS) on in vivo tissue spectra to noninvasively monitor changes in the oxygenation of the brain in the intact cat head , NIRS has been used in experimental and clinical investigations of tissue oxygenation (for a review, see  and ) with many studies on muscle oxidative metabolism (for a review, see -).
The physical principles of NIRS have been reported previously in detail (for a review, see -). Briefly, NIR light (700–1000 nm) penetrates skin, subcutaneous fat/skull, and underlying tissue such as muscle, and is either absorbed or scattered within the tissue. The relatively high attenuation of NIR light in tissue is due to: (a) O2-dependent absorption from chromophores of variable concentration, i.e., hemoglobin (Hb), myoglobin (Mb) (in muscle only), and cytochrome oxidase; (b) absorption from chromophores of fixed concentration (such as skin melanin); and (c) light scattering .
For pure absorption, the relationship between the attenuation and chromophore concentration can be described by Lambert-Beer’s law which states that the attenuation of an absorbing compound dissolved in a nonscattering solvent is directly proportional to the product of the concentration of the compound and the optical pathlength. While in media with scattering, such as tissue, multiple-scattering effects cause the physical pathlength that light travels through the tissue to be larger than the geometrical distance between the source and detector. Sometimes this physical pathlength is called the differential pathlength, which equals the distance between source and detector times a differential pathlength factor . The effect of scattering on the spectral baseline is sometimes described in a modified Lambert-Beer’s law equation by adding a term G .
Hemoglobin can exist in two main forms, oxyhemoglobin (O2Hb) and deoxyhemoglobin (HHb), each with its own optical absorption characteristics. Blood oxygen saturation is defined as SO2 = 100%×CO2Hb/(CO2Hb+ CHHb), where CO2Hb and CHHb are concentrations of O2Hb and HHb respectively, and can be measured by NIRS. To obtain absolute chromophore concentrations in tissue, the differential pathlength and the scattering term G in the modified Lambert-Beer’s law must be known.
Conventional non-spatially resolved continuous-wave (CW) NIRS (CWNIRS) only measures changes of O2Hb and HHb from an initial value by assuming a constant tissue scattering effect, thus serves only as a trend monitor. New methods are required to separate pure absorption of the hemoglobin components from scattering which is convoluted in the attenuation spectra in order to calculate absolute values for tissue oxygen saturation (StO2).
Some efforts have been made using non-spatially resolved CWNIRS to measure differential pathlength factors [14,15] to determine the absolute concentration of specific chromophores such as HHb in tissue . For absolute determination of StO2, more sophisticated techniques have been used. CW spatially resolved spectroscopic (SRS) methods are based on either broadband or discrete wavelengths using a diffusion approximation model and at least two source-detector distances [17–20]. Time-resolved spectroscopy (TRS)  and phase or frequency modulation spectroscopy (PMS)  can resolve absolute absorption and scattering and hence calculate StO2 through the time of flight of photons, or from modulated light information, respectively. But even with these methods, the accuracy of the StO2 determination can be improved because these techniques do not consistently account for the optical interference from skin pigment and adipose tissue and the effect of blood volume changes on tissue pathlength .
Non-spatially resolved CWNIRS is the simplest and most economic technique for realtime clinical monitoring of patients. CWNIRS also permits simultaneous measurement of additional parameters such as pH  and hematocrit  to be calculated from the spectra using methods such as partial least squares (PLS) regression . Recent efforts have attempted to use non-spatially resolved CW instruments to measure absolute StO2. Myers, Anderson, and Seifert et al.  employ a 4 wavelength “wide gap” second derivative spectroscopic method to remove the effect of scattering. A StO2 calibration curve, which related scaled second derivative attenuation at 720 nm to hemoglobin SO2 was produced in vitro on hemoglobin samples . This technique is limited since the scattering properties of in vivo tissue are different from the in vitro hemoglobin samples used to produce the calibration curve. Stratonnikov and Loschenov  proposed a non-spatially resolved CW spectroscopic technique to measure absolute StO2 using visible light. This method assumed that while HHb and O2Hb contributions to light attenuation are strongly variable functions of wavelength, all other contributions to the attenuation, including scattering, are smooth wavelength functions and can be approximated by a Taylor series expansion. By linear least squares fitting of the multiple-wavelength measured attenuation spectrum to the Taylor expansion attenuation model, the multiplication of pathlength with the concentrations of O2Hb and HHb can be obtained, and in turn StO2 can be calculated . This algorithm is simple and robust, and it works in the visible wavelength range (510 to 590 nm) in which O2Hb and HHb have sharp and distinct peaks; however, it was unsuccessful in the NIR wavelength range, where light can penetrate deeper inside the tissue. Neither method accounted for spectral contributions from skin pigment and fat.
It has been shown that the fat layer has significant influence on the CWNIRS in vivo muscle attenuation spectra  and StO2 [29–31]. Wassenaar and Van den Brand showed that melanin (skin pigment) clearly interferes with the in vivo CWNIRS StO2 measurement in subjects with darker skin and should be interpreted with caution . Buono, Miller and Hom et al.  showed that skin blood flow affects in vivo CWNIRS measurements in human skeletal muscle. Thus the objective of this paper is to demonstrate a simple, reliable and inexpensive technique using CWNIRS that can quantitatively measure StO2 without the interference of light absorbance and scattering from skin pigment and fat. Such an absolute muscle oxygen saturation measurement, SmO2, will allow reliable comparisons between different subjects and afford good reproducibility for the same subject. To achieve this goal, we first corrected the NIR spectra for interference from skin and fat, then expanded upon Stratonnikov and Loschenov’s method  so it performs reliably in the NIR wavelength range. The method was evaluated on simulated muscle spectra with 4 different scattering coefficients, and on in vivo forearm muscle spectra from 5 healthy volunteer subjects undergoing arterial occlusion. Repeatability was demonstrated by making 5 replicate measurements on 24 healthy subjects, each separated by at least 48 hours.
2. Methods and materials
2.1 Muscle oxygenation saturation calculation algorithm
Muscle oxygenation saturation (SmO2) is defined by:
where c (O2Hb+O2Mb) is the concentration of oxygenated heme (Hb = hemoglobin, Mb = myoglobin), c (HHb+Mb) is the concentration of deoxygenated heme and c (O2Hb+O2Mb) + c (Hb+Mb) is the total concentration of heme in the muscle. Since hemoglobin and myoglobin have very similar absorption spectra in the NIR wavelength range, no attempt was made to distinguish between myoglobin and hemoglobin contributions in the in vivo and modeled data.
The muscle attenuation spectrum in optical density (OD) units is defined as the natural logarithm of the ratio of incident light intensity (I0) to reflected light intensity (I). It can be approximated with the Taylor series expansion method described by Stratonnikov and Loschenov :
where λ is wavelength; c0 and c1 are constants, <L> is a mean pathlength of the reflected light through the tissue and μa(λ) is the absorption coefficient as a function of wavelength, and is described by Eq. (3):
where c HHb+Mb, c O2Hb+O2Mb and cwat are the concentrations of deoxygenated heme, oxygenated heme, and water in the tissue respectively, and εHHb(λ), εO2Hb(λ), and εwat(λ) are wavelength-dependent extinction coefficients for HHb, O2Hb and water respectively. Hemoglobin and myoglobin have similar extinction coefficients in the infrared region of the spectrum, so the extinction coefficients of HHb and O2Hb are also used for myoglobin in Eq. (3). The difference between Eq. (2) and the modified Lambert-Beer’s law is that in Eq. (2) <L> is considered as a Taylor coefficient which is not dependent on the absorption coefficient μa, and the model is not intended to model the dependence of <L> on μa as it is done in the modified Lambert-Beer’s law but to take into account the next (quadratic) term in Taylor series expansion .
Light source intensity I0, is estimated as the reflected light intensity from a 99% reflectance standard, Iref, when calculating measured light attenuation spectra. The measured light attenuation spectrum, Aexp(λ), is expressed as:
This reference signal, Iref, measured from the 99% reflectance standard differs from I0 in Eq. (2) by a wavelength independent constant factor resulting in the appearance of an additive constant in the experimental attenuation curve. This constant factor can be incorporated into the c0 coefficient in Eq. (2). c0 also describes the wavelength independent absorption from chromophores other than heme and water in the tissue. The function (c0 + c1 λ) in Eq. (2) describes the portion of the spectrum resulting from light which is scattered, and the additional factors described by c0. The remaining portion of Eq. (2) describes light absorption from the heme and water.
Typically, light attenuation in the target tissue arises from both light absorption and light scattering processes. Light is absorbed by hemoglobin in small blood vessels and myoglobin in cells, by both intravascular and extravascular water, and by melanin pigment in skin. Light can be scattered by physical structures such as blood vessel walls and muscle fibers, and also by fat which overlies the muscle tissue.
To calculate SmO2, we first remove the components of the spectrum resulting from skin pigment absorption and fat scattering by using a two-source, one-detector configuration fiber optic probe . One source is placed close (2.5 mm) to the fiber optic bundle which transmits light to the spectrometer. This captures light from only the skin and fat layers. The second source, a greater distance (30 mm) from the bundle transmitting light to the spectrometer, captures light from the skin, fat and muscle layers. Light collected from the short distance pair is orthogonalized with the light from the long distance pair to generate a spectrum which describes attenuation from only the muscle layer (this is termed short-distance orthogonalization). The details of this method are described in a prior publication .
The values of c0, c1 <L> as well as c HHb+Mb, c o2Hb+O2Mb, cwat are obtained by minimizing the sum of square difference χ2 between the modeled and experimental spectra with the least square method:
where λi are the N wavelength values at which the attenuation is measured in the range between λmin and λmax. Once c HHb+Mb and c O2Hb+O2Mb are obtained, SmO2 is calculated using Eq. (1).
2.2 SmO2 algorithm implementation
Stratonnikov and Loschenov  successfully obtained blood SO2 by fitting the experimental attenuation spectra collected from human fingers in the visible wavelength range (510 to 590 nm) to the modeled Taylor expansion attenuation spectra [Eq. (2)]. The disadvantage of this spectral range is that the light penetration depth is small and diffusely reflected light cannot be collected from deep tissue such as muscle with a significant fat layer on top. In the NIR wavelength range light penetrates deeper into the tissue, even through thick fat layers. Stratonnikov and Loschenov  tried to interpret their NIR data by the Taylor expansion attenuation model but failed to obtain accurate tissue StO2 measurement because their method could not distinguish the smooth broad spectral shape of O2Hb in this wavelength range from those contributed by scattering and other non-heme chromophores.
To overcome the problems that Stratonnikov and Loschenov experienced we start with skin and fat corrected spectra to help reduce the scattering effects of the fat as well as the influence of skin melanin, thus the experimental spectrum can be more accurately described by the Taylor expansion model without a quadratic or/and higher terms. Instead of using linear least squares fitting, we used a bound-constrained non-linear least squares fitting of the measured attenuation spectrum Aexp(λ) [Eq. (4)] to the modeled spectrum Amodel(λ) described by Eq. (2) to obtain values of c0, c1, <L> as well as c HHb+Mb, c O2Hb+O2Mb, and cwat. The appropriate use of constraints assists in isolation of the oxygenated heme component of the spectrum. In the NIR region light scattering (μs´, reduced scattering coefficient) can be described by a linear function of wavelength with negative slope . Meanwhile, the extinction spectrum of O2Hb monotonically increases with a positive slope (Fig. 1). Our method constrained the slope term c1 in Eq. (2) as a non-positive number, to decouple the scattering and oxygenated heme components of the attenuation spectrum.
General local deterministic non-linear least squares optimization algorithms such as gradient descent or Newton optimization algorithms are known to be sensitive to local minima, unless they are initialized close to the optimal solution. In a healthy subject, it is possible to make a good initial estimate of c HHb+Mb, c O2Hb+O2Mb, and cwat with prior knowledge of clinical data from human subjects, however, it is difficult to estimate appropriate initial values of baseline offset c0, slope c1 and average pathlength <L> because the muscle scattering properties of each subject are different.
We used a data preprocessing/optimization method that is similar to the finite-element based algorithm proposed by Iftimia and Jiang  for quantitative reconstruction of both absorption and scattering images to determine appropriate values of c0, c1 and <L> to initialize our optimization. Our adaptation of their method starts with a simple least squares minimization scheme to determine the initial values for these parameters; we refer to this as sweeping method. We fixed c HHb+Mb, c O2Hb+O2Mb, cwat according to prior knowledge of these values for healthy human subjects. We then individually varied the parameters c0, c1 and <L> over a specified range and calculated an attenuation spectrum (Acalc). As we swept the values for all 3 parameters we calculated the sum of squared differences between the experimental spectrum (Aexp) and Acalc to identify specific values for all 3 parameters that corresponded to the minimum sum of square error. These values will be the optimal initial values for the next step which is fitting the measured spectrum to the model. Performing the sweep step helps ensure that we determine the global, rather than the local minimum solution in the subsequent fitting step [Eq. (5)]. To summarize, Fig. 2 shows the scheme of the in vivo data analysis procedure.
The algorithm was implemented by programs written in version 7.0.4 of the Matlab® programming language (Mathworks Inc., Natick, MA). The extinction coefficients of HHb, O2Hb and water, which were measured by Matcher et al. [14, 37, 38], were linearly interpolated to match our spectrometer’s wavelength pixel-to-pixel resolution and then used in the SmO2 algorithm. The non-linear least squares fit used the Levenberg-Marquardt optimization method to optimize Eq. (5) and was implemented with the “lsqcurvefit” function in the Matlab® Optimization Toolbox version 3.0.2 (Mathworks Inc., Natick, MA). The Matlab® SmO2 calculation program was then compiled to an executable program using Matlab® Compiler version 4.2 which was called by the user interface program. For real time implementation of the SmO2 algorithm, only the first spectrum was used for the sweep step to reduce calculation time, the optimal initial parameter values determined with the sweep were then used as initial values for calculations on all future spectra.
2.3 Calculation of simulated tissue spectra for evaluation of SmO2 algorithm
To evaluate the accuracy of the algorithm, simulated tissue attenuation spectra were calculated for four (4) different tissue light scattering conditions, corresponding to no scattering and light scattering from the forearm, calf and head. The algorithm was applied to the simulated spectra to calculate SmO2 and this was compared to the value of SO2 established for each simulated spectrum. Only the muscle layer was simulated and hemoglobin concentration was assumed to include both hemoglobin and myoglobin. For each tissue type, values for μa(λ) described by Eq. (3) were chosen to simulate the eight different theoretical SO2 values: 0%, 10%, 20%, 40%, 50%, 60%, 80%, and 100% by varying the concentrations of HHb, O2Hb but keeping the sum of HHb and O2Hb constant (i.e., total hemoglobin concentration) and water concentration constant. Source-detector distance and μs´(λ) were also unvaried when calculating the simulated spectra. The water concentration cwat was fixed at 60% by volume , along with a source-detector spacing d of 3.0 cm, and total hemoglobin concentration of 0.1 mM. The simulation wavelength range was the same as our experimental system: 725 nm and 880 nm. The sweep method was used once for a 50% simulated SO2 spectrum to obtain the optimal initial values of the fitting parameters, then those optimal initial values were used for all remaining spectra.
To generate light attenuation spectra that corresponded to a non-scattering, absorbing tissue, a Lambert-Beer equation with terms that correspond to contributions from hemoglobin and water was used:
where Aexp(λ) is the attenuation at wavelength λ and L is the pathlength of the light through the pure absorption tissue, which is the source-detector spacing in this case.
Light attenuation spectra were also calculated for three (3) different tissues types in which light scattering occurred. A single layer infinite slab diffusion model  was used to generate light attenuation spectra Aexp(λ) for selected values of tissue μa(λ), μs´(λ), and a source-detector spacing d (and wavelength λ). This model has been previously used to evaluate NIRS algorithm performance [16, 24] and has the form:
where the quantity σ(λ) is calculated according to
Values for μs´(λ) were selected to correspond to tissues in the forearm, calf, and intact head of a human subject. The μs´(λ) for each tissue type were calculated according to Eqs. (9), (10), and (11) respectively :
In Eqs. (9)–(11), μs´(λ) is in units of cm-1 and λ is in units of nm.
2.4 In-vivo Studies
The method was evaluated in two different in-vivo studies. Arterial occlusion studies were performed at the University of Massachusetts Medical School on 5 healthy volunteers. Measurement repeatability studies were carried out on 24 healthy subjects at NASA Johnson Space Center. The studies were approved by the Institutional Review Boards at the respective institutions.
2.4.1 In vivo tissue NIR spectra measurement
The in vivo attenuation spectra for each subject were measured using a custom-fabricated two-distance fiber optic probe (Luxtec Corp., West Boylston, MA) with 2.5 mm and 30 mm source-detector separation . The subjects were illuminated with an 8.5 W tungsten lamp (model 7106-003, Welch Allyn Corp., Skaneateles, NY). A custom-made hot mirror (Opticorp, Chelmsford, MA), allowing only light between 650 and 1000 nm, separated the lamp from the fiber optic illumination cable. The mirror reflects light of both shorter and longer wavelengths, which would heat the skin. The filtered light was then passed through either the long distance fiber bundle (diameter, 3.5 mm.) or the short distance bundle (diameter, 1.0 mm). The two source fiber bundles were placed at either an on-axis, or off-axis orientation from the lamp filament. A computer controlled shutter was used to switch between the two source fiber positions alternatively with the control of the interface software so only one source bundle was illuminated by the lamp at a time. The light reflected from the muscle passed through a 1.0 mm fiber bundle and was detected with a commercially available spectrometer (USB2000, Ocean Optics Inc., Dunedin, FL) which has a grating with a density of 600 grooves/mm, a 2048-element linear CCD-array detector, and a 200 μm slit, thus providing a dispersion of 0.3 nm/pixel and optical resolution of 7.6 nm over the wavelength range 590 – 1245 nm. For our calculations only the wavelength range 725 – 880 nm was used. Custom user interface software was coded in Visual Basic (Microsoft Inc., Redmond, WA) and used to collect the diffuse reflectance spectra.
For each subject the integration time was selected to maximize the intensity of the light reflected to the spectrometer. Since the optimum integration time varied across the different subjects due to variations in the sampled tissue, the measured spectra from the tissue were normalized through division by the integration time. Broadband tissue attenuation spectra, were calculated by comparing the count rate (counts/integration time) of the detected radiation to the count rate from a 99% diffuse reflectance reference standard (Model SRT-99-050, Labsphere Inc., North Sutton, NH). Reference spectra were collected from the standard by placing the probe at a predetermined and fixed height above the standard. The optimum height for the long-distance fiber was different from the best height for the short-distance fiber. The optimal heights were determined using the method described in reference . The attenuation spectrum Aexp(λ) is calculated with Eq. (12).
where Ir (λ) and Is (λ) are the count rates for the reference and sample measurements at wavelength λ respectively.
SmO2 is then determined from the deep muscle attenuation spectra after short-distance orthogonalization.
2.4.2 Arterial occlusion
The SmO2 algorithm was applied to NIR spectra acquired from 5 healthy volunteer subjects (2 females and 3 males; 1 African-American, 2 Asians and 2 Caucasians) during arterial occlusion. While each subject was in a supine position, an arm cuff controlled by an automatic tourniquet system (Zimmer ATS 1500, Zimmer Inc., Warsaw, IN) was placed on the upper right forearm, above the elbow and secured in place. The NIRS probe was placed on the skin surface overlying the subject’s right FDP muscle, after locating the muscle through fingertips flexing. Baseline measurements were collected for 5 min. Arterial occlusion was established by rapidly increasing the pressure in the cuff to 90mmHg above the subject’s systolic blood pressure. This pressure was maintained for 10–15 minutes. The pressure was then released and spectra were collected for another 5 minutes. NIR tissue spectra were acquired every 25 seconds. SmO2 at baseline, 5 minutes ischemia, 10 minutes ischemia and at maximum hyperemia were obtained from the recorded results after the study was completed.
2.4.3 Repeatability study
Spectra were collected and analyzed from twenty-four (24) healthy subjects (15 males and 9 females) who were enrolled in a hand-grip exercise study, prior to performing any exercise. With each subject lying in a prone position, the NIRS probe was place on the skin surface overlying the subject’s right FDP muscle, after locating the muscle by asking the subject to flex their fingertips. Subject positioning and hand orientation were standardized across days. NIR tissue spectra were acquired every few seconds for 10 minutes. Resting SmO2 was calculated and averaged for spectra collected during minutes 5–9 of this baseline period. The subject returned to lab 4 more times to repeat the measurement. Each repetition was separated by a minimum of 48 hours. Subjects were instructed to be well hydrated and refrain from exercise on the day of testing.
The coefficient of determination (R2) between the real and calculated values of SO2 for each simulated tissue type was calculated to assess the accuracy of SO2 determined by fitting the simulated light attenuation spectra to the Taylor expansion attenuation model. In addition, values of the root-mean-square error of prediction (RMSEP), which describes the estimated measurement error, were calculated according to Eq. (13):
where N is the number of light attenuation spectra, and ŷi and yi are estimated and set values of SO2, respectively. Values of R 2 near one and relatively small values of RMSEP indicate that the estimated SO2 values are accurate.
For in vivo studies our results, as well as those obtained from other authors, were expressed as mean ± standard deviation.
3. Results and discussion
3.1 Results from simulated spectra
Figure 3 shows the simulated muscle attenuation spectra for a series of set values for SO2. Figure 3(a) is calculated using Eq. (6) showing spectra from tissue that does not scatter incident light (e.g., light attenuation occurs by absorption only). The remaining portions of Fig. 3 are calculated using Eqs. (7)–(11) which corresponded to tissue that have the scattering properties of (b) forearm, (c) calf and (d) intact head. The spectral shapes calculated for tissue with scattering are similar to the spectral shape without scattering for the same SO2 values. When tissue scattering is added to the simulated spectra the attenuation significantly increases. Additionally, the variation in the scattering coefficient for different tissue types impacts the attenuation spectra in a nonlinear fashion as SO2 increases.
Figure 4 shows the plot of real versus estimated SO2 for simulated spectra with pure absorption, and with forearm, calf and intact head scattering properties. The diagonal line in the figure represents a perfect match between the real and predicted SO2 values. Table 1 lists the R2 and RMSEP between the real and estimated SO2 for each set of simulated spectra.
The predicted results of SO2 for all simulated spectra with varying scattering properties were in good agreement with their actual values. The predicted results were clustered along the line of perfect prediction (Fig. 4) with excellent correlation. The predicted measurement accuracy, RMSEP is less than 5.5 % SO2 for all cases, and the simulation of scattering from the calf is equivalent in accuracy to prediction from spectra with no scattering. Stratonnikov and Loschenov  evaluated their original method on NIR spectra, reporting that it was inaccurate in this wavelength region. They collected in vivo spectra on the finger during arterial occlusion but their calculation resulted in erroneously high baseline values in healthy subjects, concluding that their method had limitations for use in the NIR. Our modifications to their method successfully predicted SO2 values over the entire SO2 range (0–100%) and for a variety of scattering coefficients in the simulated spectra. The following sections describe application of our method to in-vivo spectra.
3.2 Results of arterial occlusion study
Figure 5 shows a set of attenuation spectra collected from an African American subject in the arterial occlusion study (a) before and (b) after skin and fat correction. It can be seen that after the skin and fat correction, the spectra become more coincident as the attenuation caused by fat scattering and the absorption of skin pigment between 725 and 750 nm were removed.
Figure 6 shows (a) the calculated SmO2 values during the arterial occlusion study for the Africa American subject whose spectra are shown in Fig. 5, and (b) a comparison of the measured skin and fat corrected spectrum with the fitted and residual attenuation spectrum. The measured spectrum is well fitted by the model and the residual spectrum is small.
Figure 6(a) shows that during the arterial occlusion (ischemia), SmO2 declined progressively, reaching a plateau near 12% for this subject. After the occlusion was released (hyperemia), the SmO2 increased progressively and reached a peak value at approximately 2 minutes after the release of the occlusion. This subject’s minimum SmO2 was not zero during the occlusion, while some other subjects did reach a minimum SmO2 of zero.
A summary of the mean SmO2 values at baseline, 5 minutes of ischemia, 10 minutes of ischemia and maximum hyperemia for the 5 subjects are shown in Table 2 along with published data collected with frequency-modulated and time-resolved NIRS systems [41, 42].
Stratonnikov and Loschenov  obtained a baseline SO2 of 65% from visible spectra which is comparable to our baseline results of 68.9% from NIR spectra; however, when NIR spectra were used, they obtained abnormally high baseline SO2 values of 85%–100%. Visible spectra provide suitable results for anatomical regions with thin fat layers, such as the finger, but are unsuitable for studies where the tissue is covered with a thick fat layer, such as the leg.
DeBlasi et al.  used a phase modulated multi-distance NIRS technique while Hamaoka et al.  used time-resolved NIRS. Our results compare well with results obtained by these authors. It has been shown that the phase modulated multi-distance NIRS technique can obtain a spectroscopic signal that primarily represents the muscle layer if the fat layer is less than a few mm thickness . The agreement with DeBlasi’s result  likely indicates that fat thickness for their subjects was not too thick. Even though Hamaoka’s TRS method  did not use an explicit correction for fat, their technique may determine an “effective” scattering coefficient for all layers, including the fat. As long as the fat layer is thin and light penetrates to the muscle this may be sufficient. This technique, however, did not address absorption by skin pigment. A skin pigment correction is required for accurate, absolute measurement on subjects with dark skin. It is likely that all subjects in their study were Caucasian, while only 40% of our subjects were Caucasian.
In our study the average %SmO2 at 10 minutes ischemia was 14.2 ± 14.8 % (range 0 – 31%). In the DeBlasi study , the average SmO2 at 12 minutes occlusion was 24.1 ± 12.5 %, similar to our result. SmO2 of zero is not expected for all subjects, since there are some vessels in the muscle which do not exchange oxygen with the tissue and we can expect that there is significant heterogeneity in vascular distribution between subjects. Additionally, it is difficult to reliably achieve complete arterial occlusion in some subjects, particularly those with cardiovascular disease. Cardiovascular disease can “harden” the arteries, making them difficult to compress completely.
3.3 Results for repeatability study
The average standard deviation for 5 placements for each of the 24 subjects is 4.7%. Analysis of variance showed that there were no measurement trends with time. The placement error is relatively small and is most likely a result of slight differences in anatomical structure under each sensor placement position. The actual placement error may be even smaller, since SmO2 is a function of a number of parameters that effect oxygen extraction by muscle cells. However, we attempted to minimize these factors by asking the subjects to refrain from exercise before measurement and come to the lab well hydrated.
Additionally, the distribution of average SmO2 measurements across the 24 healthy subjects is also small: 66.1% ± 4.0%. Table 3 compares the baseline StO2 measured on the forearm of healthy human subjects from our study (SmO2) with data from studies using other commercially available NIRS instruments. It can be seen that our results are comparable to those obtained with PMS, TRS and SRS instruments [41, 42, 45, 46].
Crookes et al.  and Creteur et al.  used wide gap second derivative CW single-distance system  to measure StO2 in the thenar eminence. Their StO2 values were higher than other absolute StO2 spectroscopy techniques listed in Table 3 and significantly higher than SO2 determined for capillary blood . It is possible that StO2 is higher in the hand, than the forearm, but it is also possible that this difference is a result of the in vitro determined calibration curve used in the InSpectra instrument . The average StO2 value Crookes et al. obtained was 87% ± 6%, even higher than the value of 78.3± 6.8% from the Creteur et al.  study. In Crookes’ study , 89.7% of the 707 healthy subjects were Hispanic or Black, so the abnormally high StO2 determination for these subjects may be caused by inadequate compensation for skin pigmentation. We suggest that the spectral correction for skin pigment and fat scattering, coupled with methods that accurately model scattering in muscle are key to making reliable measurements on humans subjects with CW techniques.
The dual-distance technique described here was developed for the purpose of quantitative determination of SmO2. The technique requires that light collected with the short source-detector distance pair only contain information from the skin and fat layer, and not the muscle layer. The technique will have greater error if used on people with very thin fat layers (< 3 mm).
Similarly, the technique may not work well for determination of cerebral oxygen saturation, even with an optimized short source-detector spacing, since there is considerable variability in the amount of cerebral-spinal fluid between the skull and the brain .
We have demonstrated a new, non-invasive method for the absolute determination of SmO2 from skin and fat-corrected broadband CWNIRS. This method is different from other spatially resolved algorithms in that the diffusion approximation based attenuation model is not employed in the calculation. The method is an extension of the Stratonnikov and Loschenov method  of fitting an experimental attenuation spectrum to a Taylor expansion attenuation model. We extend this method to the NIR range by employing skin and fat corrections to the spectra prior to fitting, applying constraints to key fitting parameters and optimizing initial values for the first spectrum only, allowing the technique to be implemented in real-time. We have shown that the algorithms accurately predict SO2 on simulated muscle spectra. We have also obtained SmO2 results on in vivo tissue spectra comparable with others who have used more complex and expensive instruments. We further demonstrated that the technique is repeatable over multiple placements on the same individuals and produces well controlled values across a cohort of 24 subjects. The method is implemented with simple, economical equipment allowing it to be easily applied to bedside and field monitoring.
This work was supported by the National Space Biomedical Research Institute (NSBRI) through NASA cooperative agreement NCC 9-58. We’d like to acknowledge Patrick Phillipps, Sherry Grobstein and Luxtec Corporation,West Boylston, MA for their technical assistance with the design and fabrication of the tissue oximeter hardware and user interface software.
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