Frequency-domain multichannel optical detector for non invasive tissue spectroscopy and oximetry

The concentration calculated using the extinction coefficient of Abstract. We have designed a multisource frequency-domain spectrometer for the optical study of biological tissues. Eight multiplexed, intensity- modulated LEDs are employed as the light sources. Four of them emit light at a peak wavelength of 715 nm (Xi); the other four, 850 nm (X2). The frequency of intensity modulation is 120 MHz. This instrument measures the frequency-domain parameters phase, dc intensity, and ac am- plitude at the two wavelengths X and X2 and for different distances between light source and detector. From these frequency-domain raw data, the absolute values of the absorption and reduced scattering coefficients of tissue at X1 and X2 are obtained. The oxy- and deoxyhemoglobin concentrations, and hence the hemoglobin saturation, are then analytically derived from the molar extinction coefficients. Acquisition times as short as hundreds of milliseconds provide real-time monitoring of the measured parameters. We performed a systematic test in vitro to quantify the precision and accuracy of the instrument reading. We also report in vivo measurements. This spectrometer can be packaged as a compact portable unit.


Introduction
The determination of the optical properties of tissues is of fundamental importance in many fields in medicine for both diagnostics and monitoring.' Different wavelengths of light penetrate tissue preferentially. In the near infrared region, ranging from 700 to 900 nm, light penetrates several centimeters. Consequently, spectroscopic methods can, in principle, be used to measure the concentration oftypical tissue constituents, such as hemoglobin, which present absorption bands in that spectral region. The most important characteristic of every apparatus aimed at the measurement of optical properties of tissues is that is must provide quantitative information about a medically important parameter, for example, the concentration of oxygenated and deoxygenated hemoglobin, of glucose, or of other typical tissue constituents.
In standard spectroscopic practice, when light extinction is mainly due to absorption, the absolute determination of the concentration of an absorber can be obtained by a measurement of the light transmitted through a sample of known thickness. A transmission measurement enables one to determine the absorption coefficient from the Beer-Lambert law. The concentration of the absorber can be calculated using the molar extinction coefficient of the absorber. If more than Abstract. We have designed a multisource frequency-domain spectrometer for the optical study of biological tissues. Eight multiplexed, intensitymodulated LEDs are employed as the light sources. Four of them emit light at a peak wavelength of 715 nm (Xi); the other four, 850 nm (X2). The frequency of intensity modulation is 120 MHz. This instrument measures the frequency-domain parameters phase, dc intensity, and ac amplitude at the two wavelengths X and X2 and for different distances between light source and detector. From these frequency-domain raw data, the absolute values of the absorption and reduced scattering coefficients of tissue at X1 and X2 are obtained. The oxy-and deoxyhemoglobin concentrations, and hence the hemoglobin saturation, are then analytically derived from the molar extinction coefficients. Acquisition times as short as hundreds of milliseconds provide real-time monitoring of the measured parameters. We performed a systematic test in vitro to quantify the precision and accuracy of the instrument reading. We also report in vivo measurements. This spectrometer can be packaged as a compact portable unit.
one absorber is present, measurements at different wavelengths can provide a method to determine the concentration of all different noninteracting absorbing chemical species present in solution, provided they have different absorption spectra. The success of this method depends on the precision of the measurement and on the number of different substances that are present.
In tissue spectroscopy the problem is more complex. A measurement of the light transmitted through a slab of tissue is not possible using noninvasive methods, except for special thin regions ofthe body. Moreover, the amount of transmitted light depends not only on the absorption of the medium, but also on its scattering properties. This fact is particularly important when, as for most tissues in the near infrared, the scattering coefficient far exceeds the absorption coefficient. Several different methods have been proposed to take account of the scattered light. For example, empirical corrections based on the type oftissue have been used to take into account the effect of scattering on the absorption properties.2 Reflectance spectrophotometry has been performed,3 and theoretical models have been used to calculate the diffuse reflectance of light from tissues. 4 The success of these methods has been marginal, although there are a number of commercial instruments based on them. The major problem with the proposed approaches is that, in order to obtain a reasonable estimate of the concentration of a substance in tissue, some sort of a priori calibration must be performed, based on the statistical analysis of a large number of samples. In practice, unpredictable results are frequently obtained. Instead, an of the concentration of chromophores, independently of fac-2. LEDs as the intensity-modulated light sources: LEDs tors such as the color of the skin or the amount of lipids in are attractive light sources for practical applications the tissue. because of their safety, reliability, ease of modulation, A few years ago, a new approach was proposed to deter-stable output, and low mine the optical properties of tissues.58 The basic idea is to use time-resolved methods to separate scattering from absorption. The time-resolved measurements can be made in either the time domain or the frequency domain. In the time domain one measures the time-of-flight distribution of a light pulse between a source optical fiber and a detector fiber.9 In the frequency domain one measures the phase delay of asinusoidally modulated light source between the source and the detector, and the attenuation of the average intensity and of the amplitude of the intensity It has been shown that, under some assumptions, the average time of flight is equivalent to a phase delay measurement at a given 1 1 The major advance came from the development of a rigorous mathematical model for the description of light transport in turbid media, which allowed for a better understanding of how the measurable parameters in time-resolved spectnoscopy are related to the scattering and absorption coefficients of the medium5"2 This model is based on the as-Multiple source-detector separations: A simple method to measure the absolute values ofthe scattering and absorption coefficients is to determine the slopes of the straight lines associated with dc, ac, and phase. The linear relationships between measurable quantities in frequency-domain spectroscopy and the sourcedetector distance r have been derived elsewhere.'5 For convenience, we report a brief summary of the denvation in the appendix. The measurement of the slopes of these straight lines as a function of r requires several (at least two) source-detector separations; 4. Appropriate modulation frequency: A frequencydomain spectrometer requires the intensity of the light source to be modulated at a certain radio frequency. The value of that frequency affects the sensitivity of the instrumentation and the signal-to-noise ratio, and hence must be chosen with cane.
sumption that the distribution of photons in strongly scattening media is well described using diffusion theory.
In the near infrared, low-cost sources such as light-We designed the instrument by careful consideration of each one of the four above features. emitting diodes can be modulated at frequencies high enough to realiably measure the opticalparameters oftissues.'3 Using Feature 1 Our specific goal is to determine the concenthe frequency-domain method and the diffusion theory, the trations ofthe oxygenated (HbO2]) and deoxygenated ([Hb]) absorption spectrum of a chromophore was quantitatively forms of hemoglobin using the methods we previously derecovered even in the presence of a concentration of scattering particles similar to those found in tissues.' Furthermore, we veloped for the measurement of the optical parameters pa (absorption coefficient) and p (reduced scattering coeffihave shown that the accuracy of a measurement is increased cient) in tissues. We assume that the main contribution to if several source-detector separations are The absorption in tissues in the near infrared region is due to case of a semi-infinite geometry, which is a model of the hemoglobin, thus writing noninvasive in vivo configuration, has been studied both in the time domain5 and in the frequency domain.'5 As a result, }-' bo2[Hb021 + EHb[I (1) the relationships between the phase and attenuation of the photon density wave on one hand and the optical properties where EHbO2 and EHb are the extinction coefficients at waveof the medium on the other have been determined for such length X for oxy-and deoxyhemoglobin respectively. For a boundary condition. example, this assumption is valid for wavelengths in the near In the present paper, we describe an LED-based frequencydomain spectrometer for the direct determination of the oxy-infrared for the mammalian brain, where the contribution of myoglobin and of other tissue constituents is minimal.'6"7 and deoxyhemoglobin content in tissues. Once the concen-Equation (1) clearly shows that a single measurement is not trations of these two chemical species are separately known, sufficient to provide both [Hb02] and [HbI. Instead, both the amount of hemoglobin saturation and tissue hemoglobin species can be determined by measuring the absorption coefcontent can be determined. The principle presented here is not limited to the measurement of these two substances, but ficient at two different wavelengths X, and X2. The two equations for p and i2 then yield the following equations: can be extended to the measurement of other chromophores by properly choosing the wavelengths of the light sources. We also conducted an experimental test to study precision (2) and accuracy of the instrument.

Description of the Instrument
We designed a frequency-domain spectrometer for direct (3) . measurement of oxy-and deoxyhemoglobin content in tissue based on the following features: We want to perform measurements in the spectral region from 700 to 900 nm, in which light transmission is sufficient to 1 . Measurement at two wavelengths: The determination of the concentration of two chemical species, namely oxy-and deoxyhemoglobin, requires the measurement of the absorption coefficient at a minimum of two different wavelengths.
provide both a large penetration depth (several centimeters) and an acceptable detected intensity. At shorter wavelengths (X<700 nm) the extinction coefficient of hemoglobin becomes much higher, ' 8 thus limiting penetration. At longer wavelengths (X>900 nm) the absorption of water domi- nates. 19 We also want to minimize the errors in [Hb021 and [Hb], which are related to the experimental uncertainties in the determination of i' and p2 as stated by Eqs. (2) Fig. 1, where the errors in p' and X2are set equal to 0.001 cm .
Feature 2. The feasibility of using LEDs as light sources in frequency-domain tissue spectroscopy has already been 1 3 Commercially available LEDs cover the optical window from 700 to 900 nm almost continuously. We chose two emission wavelengths that maximize the precision of the measurement of {Hb02] and [HbI. The LEDs used were the following: 1. LED Hewlett Packard HEMT-6000 (Xral = 715 nm), 2. LED Motorola MFOE 1203 (Xrk = 850 nm).
These LEDs can be efficiently modulated up to about 120 MHz by driving them with a low-voltage oscillating signal. We emphasize that the average optical power emitted by LEDs is usually less than a few milliwatts and is distributed over a wide solid angle. These properties make LEDs particularly safe in medical applications. The emission from LEDs has different ANSI standards than the emission from lasers. source and detector) associated with dc, ac, and phase, we have designed a spectrometer that employs eight different light sources placed at different distances from the detector fiber bundle, as shown in Fig. 2. The detector fiber bundle (3 mm in diameter, 0.56 numerical aperture) is connected to a photomultiplier tube. The eight sources are arranged in two parallel rows offour LEDs: in the first (second) row we placed the 7 15-nm (850-nm) LEDs, so that each row implements the measurement ofthe slopes at one wavelength. The sourcedetector distances in each row range from 1 .5 to 3.5 cm, and a light shield is placed between sources and detector to prevent reflected light from being detected. The two rows are placed as close as possible to each other in order to explore essentially the same region of the sample. The eight sources are turned on one at a time in rapid succession, using the multiplexer circuit shown in Fig. 3. The clock signal from the computer (whose frequency can be selected by software and is synchronous with the cross-conelation frequency introduced in the following paragraph) is the input of a counter (RCA CD4024), which drives a demultiplexer (RCA 74HCT238) with eight outputs connected to eight relays (Magnecraft W171DIP-2). The relays, which are closed one at a time, are in series with each LED. The result is that the LEDs are turned on in sequence at the frequency of the clock. In order to start the sequence always with the same LED, the counter is reset by a pulse sent by the computer at the beginning of the measurement. Resistors R1 to R8 in Fig. 3 are added to decrease the cunent in some of the light sources in order to have comparable light intensities at the detector fiber from each LED. This procedure of light-source equilibration allowed us to use the entire dynamic range of the analog-todigital converter. the measured quantities (slopes SdC, Sac, S) to the absorption and scattering coefficients. The photomultiplier-tube gain is modulated at a frequency of 120.0004 MHz. This method produces a beating of the 120-MHz modulated current in the detector photomultiplier with the 120.0004-MHz radiofrequency signal injected at the photomultiplier second dynode, as shown in the instrument block diagram of Fig. 4. The photomultiplier-tube output is fed to an ISS Model A2D data acquisition card inserted in the personal computer, featuring current-to-voltage converters, signal amplification stage, and a 12-bit analog-to-digital converter. The 400-Hz low-frequency component of the photomultiplier outputthe cross-correlation frequency-is isolated by using a variable-bandwidth digital filter and is digitized through a fast Fourier transform routine. Each of the eight light sources is turned on for a time that is an exact multiple ofthe 400-Hz wave period, i.e., a multiple of 2.5 ms. In a typical measurement, from a minimum of 8 to a maximum of about 50 periods of the 400-Hz wave were collected per diode, depending on the light intensity in the tissue. Each period of the 400-Hz wave is digitized at 16 points. All the collected periods at 400 Hz are averaged together, giving an average wave consisting of 16 points. At the end ofthis acquisition process, the 16-point wave is transformed using a fast Fourier transform algorithm to give the values of dc, ac, and phase of the fundamental harmonic frequency of 400 Hz. This process is repeated for each one of the light sources, yielding the values of dc, ac, and phase for all the eight LEDs. The multiplexer clock is driven by the same ISS card that performs the sampling of the photomultiplier signal, in such a way that the sampling and multiplexer clocks are synchronous. At this point, the slopes SdC, Sac, and S associated with dc, ac, and phase are computed as described elsewhere'5 (see also the appendix). Once the slopes are known, the absolute values of the scattering and absorption coefficients at the two source wavelengths are obtained using either the (I,dc) or the (F,ac) pairs (see the appendix for details). The entire process is then repeated to provide continuous monitoring of the scattering and absorption coefficients values. From the absorption coefficients, one can calculate the absolute concentrations of the oxy-and deoxyhemoglobin using the relationships (2) and (3). From the concentration of the oxy and deoxy species, the hemoglobin saturation Y and the total hemoglobin content (THC) can be obtained from the following relationships: [HbO2] Y= X100% [Hb] + [Hb021 The above discussion requires that the four LEDs at the same wavelength be identical: same dc0, ac0, (dc, ac, t measured at r= 0). This is not the case, because the LEDs can differ one from another and, as already discussed, we OPTICAL ENGINEERING/January 1995/Vol. x100% , (4) accomplished light-source equilibration by driving each LED with different currents. Therefore, we must calibrate the light intensity and the phase of the eight light sources. The calibration is performed by placing the measurement head on a solid block of a substance of known absorption and scattering coefficients. The values of the optical properties of the calibration block (made of a polymerizable glue) are measured by using a single intensity-modulated light source. This light source is placed on the surface of the block and is moved to different positions with respect to the detector (which is also placed on the surface of the block) to provide data relative to several source-detector separations. The diffusion model for the semi-infinite geometry (see the appendix and Ref. 15) is then applied to obtain ia and p at the wavelength of the light source. In this fashion, we obtained the following values for the optical parameters of the calibration block at the two wavelengths of interest: p(7l5 nm) = 0.021 cm , nm) = 0.024 cm ', jj(715 nm) = 1.94 cm ', i(85O nm) = 1 .63 cm '. It is desirable that the optical properties of the calibration block be similar to those of the investigated sample. In this way, the light intensity detected on the sample is similar to that collected on the calibration block.
When the measuring head of the tissue oximeter is placed on the calibration block, multiplicative factors for the dc and ac intensities and additive factors for the phases of the light sources are introduced in the computer in order to reproduce the known values of Ia and p. Note that this calibration is performed with the purpose of determining the intensity and the phase of each light source. This calibration procedure should not be confused with the calibration of most commercial oximeters, which need to be calibrated according to O-to-100% baselines and statistical tables based on the spectroscopic characteristics of the particular tissue to be measured. We also periodically checked the light-source calibration for drifts in the light-source characteristics.
A photograph of a prototype of the instrument measurement head is shown in Fig. 5. 3 Instrument Performance

Precision
The precision of the ji and p determination depends on the level of the detected signal and on the acquisition time. We pointed out that we are injecting more current in the more distant LEDs so as to have comparable signals from all of the light sources. We define the acquisition time t to be the time required to obtain Pa and at both X and X2. We have verified that the instrument is shot-noise limited, so that the precision varies as the square root of the product of detected signal and acquisition time. To quantify the precision of the instrument, we have measured ia and ji at a signal level of about 10% ofthe full-scale signal(i.e., the signal that saturates the analog-to-digital converter) and for different acquisition times. The experiment was performed on the same solid block used to perform the light calibration procedure. The estimated relative standard deviation uncertainties r in

Accuracy
The accuracy of the instrument is the capability of measuring values of Pa and that reproduce the actual values of and iofthe medium. Several factors influence the accuracy: 1. validity of the physical model 2. cross talk between channels 3. optical coupling between the light sources and the medium 4. wide spectral emission of the LEDs. 1 : The accuracy of the employed relationships between the frequency-domain parameters (dc, ac, and phase) and the optical properties of the medium (ia, PUs' and the index of refraction) relies on the validity of the assumptions made in deriving them. These assumptions are the macroscopic hornogeneity of the medium and the semi-infinite geometry. '5 Neither condition is rigorously satisfied in the case of in vivo measurements. Nevertheless, it has been proposed that some tissues can be treated as homogeneous media.5'2° That is not true in the presence of macroscopic inhomogeneties whose optical properties are strongly different from those of the surrounding tissue, as is the case of tumors, large blood yessels, or the vicinity of bones. Moreover, the tissue must be at least several centimeters thick to permit one to apply the equations for the semi-infinite geometry. The actual air-tissue interface is not a geometrical plane, and source and detector are not located exactly on the boundary plane. However, we have demonstrated that the measured phase and dc and ac photon fluxes are largely insensitive to the precise geometrical configuration at the The overall accuracy of the measurement in the macroscopically homogeneous, semi-infinite medium in the diffusion model has been shown to be better than 4% for p (in the range 0.02 to 0.40 cm and better than 15% for (in the range 4 to 16 cm 1)15 2: We have minimized the cross talk between consecutive channels (corresponding to the eight light sources) by disregarding each first period of the 400-Hz cross-correlation wave after switching between LEDs. This procedure has the effect of ignoring data collected during the first 2.5 ms following the switch between two LEDs. In this way, we have achieved a measured cross talk of less than 0.5%.

3:
The optical coupling between the light sources and the medium strongly affects the amount of detected light. None-(6) theless, when the LEDs are all evenly coupled to the medium, the effect on the measured values of and is on the order of a few percent. The reason this effect is so small is the insensitivity of the straight lines associated with dc, ac, and (7) phase (which are employed for determining pa and ) to the light-source intensity. In regard to in vivo applications, we have determined that the physical contact of the LEDs with the skin is not critical. This insensitivity, which is very important for quantitative measurements, is shown in Fig. 7, where we report the results obtained for the dc intensity, (8) IaO'i), Ia(X2 ), JL;(x,), and i(X2 ) in four different conditions of optical coupling between LEDs and tissue. By contrast, (9) when the optical coupling is not equal for the eight LEDs, the measured values of Pa and can be affected by systematic error. This error, estimated to be less than about 20%, must be considered when the LED-skin contact is varied unevenly over the eight LEDs.
4: Rigorously, the equations utilized to calulate and II; are valid only if monochromatic light is employed. The wide spectral emission of the LEDs (about 40 nm FWHM) introduces contributions to the measured frequency-domain parameters that are not taken into account by our theoretical model. However, the single-wavelength equations are still exact if the absorption and reduced scattering coefficients of the medium are wavelength independent. In tissues, i is 1 a weak function of X, but is wavelength dependent (even though the opposite spectral dependencies of Hb02 and Hb in the region from 700 to 900 nm partially compensate). We have simulated a realistic condition for biological tissues in conjunction with a light-source spectral distribution typical of an LED and with the spectral response of our detector. We have found that by using the singlewavelength equations in these experimental conditions, p  Fig. 7 Evaluation of the sensitivity of the measured optical coeffidents to the optical coupling between LEDs and tissue. The instrument was located on the thigh of a human subject. In trial 1 a firm pressure was applied, and this pressure was progressively decreased between successive trials. In trial 4 the LEDs were barely touching the skin. Considering trial 1 as a reference, one can observe that though the pressure strongly affects the detected intensity, it has little effect on the measured values of absorption and scattering coefficients. at 715 nm is overestimated by about 5%, but at 850 nm is underestimated by about 3%. The effect on i is less than 1%. We note that the systematic error due to the wide spectral emission of the source depends only on spectral shapes of F1aO), i(X), S(X), and F(X) (where S is the source intensity and F is the spectral response of the detector). Any scale factors in S and F, which may depend for instance on the LED-tissue optical coupling or on the voltage supplied to the PMT, have no effect on the calculated values of 11a and p. Such scale factors cancel out in the deviation of and 11. The use of laser diodes as the light sources would eliminate this bandwidth-dependent contribution to the instrumental accuracy.

Test in Vitro
We have tested our instrument by measuring the optical coefficients of a tissuelike phantom consisting of an aqueous solution of Liposyn 20% (from Abbott Laboratories) and black India ink. The medium was held in a 3.8-1 cylindrical container 20 cm in diameter. We employed several concentrations of Liposyn (13 to 50 mill) to vary , and different concentrations of a prediluted black India ink solution (0.26 to 1 .06 ml/l) to vary In this way we tested the instrument over a range of values of and Specifically, we conducted eight measurements: the first four relative to four different Liposyn concentrations in the absence ofblack India ink, and the last four relative to four different ink concentrations and the same Liposyn concentration of 50 mi/i. The conditions for each of the eight measurements are listed in Table 1 . The measuring head was placed on the surface of the turbid medium, and we verified that its positioning with respect to the surface is not critical. The measured values of Pa and jj are essentially unaffected by slightly tilting, raising, or lowering the head relative to the surface. To evaluate the accuracy of the measurements, we have also measured and i in a quasi-infinite geometry by deeply immersing a single LED and the detector optical fiber inside the medium. In this case, multiple source-detector separations were accomplished by physically moving the LED to different positions relative to the detector fiber. This technique has a!ready been described, and it provides accurate values for ia and We have estimated that in these specific experimental conditions (Liposyn as the scattering substance, water and black India ink as the absorbers, known LED emission and PMT gain-function spectral shapes) the systematic error introduced by using the single-wavelength equations is within the measurement noise. The experimental results for and II; are shown in Figs. 8 and 9 respectively. Since the results in the infinite geometry are known to be accurate,12'14 Figs. 8 and 9 provide information on the accuracy of the instrument, on its ability to separate the absorption from the scattering properties of the medium, and on the lack of correlation when one of the two parameters is changed while the other is kept constant.

Test in Vivo
Some of the results already presented were obtained from in vivo measurements. Specifically, the study of the effect of the optical coupling between LEDs and tissues (see Fig. 7) was conducted by applying the instrument on the thigh of a human subject. Wehave also used our instrument to measure the temporal behavior of the oxygenation of the forearm skeletal muscle during ischemia. For this purpose the instrument was placed on the forearm of a volunteer and a pneumatic cuff was used to induce a vascular occlusion causing ischemia. In the measurement protocol, after one minute of baseline acquisition, the cuff was inflated to a pressure of 240 to 260 mm Hg and kept inflated for eight minutes. Then, the cuff was released and data acquired for three more minutes. The acquisition time was set to 1 s. The result for the temporal evolution of hemoglobin saturation during this experimental protocol in vivo is shown in Fig. 10. For measurements 1-4, in the absence of black India ink (i.e., at low values of a)' the agreement between the infinitegeometry results and the instrument readings is very good. The value of ji is essentially due to the absorbance of water at the measured wavelength. We point out that the spectral response of the PMT we employed (Hamamatsu R928) plays a role here. While that response is relatively constant in the region from 660 to 760 nm, it drops by more than one order of magnitude from 800 to 900 nm. Taking into account the photomultiplier response, the measured peak wavelengths of the LEDs we utilized are 715 and 825 nm. The values of the absorption coefficients of water at 715 and 825 nm (0.0088 and 0.028 cm respectively21) are close to the values we measured in the absence of ink. Note that the measured values of ia are not affected by Liposyn content, which increases linearly from measurement 1 to measurement 4. By contrast, .L; linearly increases as a function of scatterer concentration, as expected.
In measurements 5-8, the second series, in which black India ink was added to increase ia the instrument readings for start to deviate from the infinite-geometry results. These deviations systematically increase with increasing pa and are larger for the 715-nm LEDs than for the 850-nm LEDs. The maximum deviation (measurement 8) is about 25% for the 715-nm LED, and about 12% for the 850-nm LED. On the other hand, the instrument readings for essentially reproduce the infinite-geometry results. The expected qualitative results (linear dependence of and nondependence of on ink concentration) are reproduced. The deviation between the values of measured with our tissue spectrometer and the results obtained in the infinite geometry (see Fig. 8) are larger than expected. These deviations should have been less'5 than 4%. We ascribe this effect to the fact that we covered the surface of the measuring head with a thin layer of transparent flexible plastic to protect the device from contamination by the liquid phantom. This layer could wrinkle, causing unpredictable (even if small) effects on its transmission properties. We performed a few measurements without the protective coating. In this case, the deviations between the instrument readings and the infinite geometry results were within the expected range. Since the prototype measurement head is not waterproof, an extended series of measurements on a liquid phantom is not possible with it. Measurements on human tissues, however, do not pose this problem.
On the basis of these experimental results and of the discussion in Sec. 3, we have estimated the uncertainties in the measured quantities i0, p, Y, [Hb021, [HbI, and THC. We distinguish the case of an absolute measurement, in which a direct reading is considered, from the case of a differential measurement, in which the difference between two readings is considered. In the latter case there is no contribution from systematic errors, and the uncertainties are due to instrument noise. Our estimates for the uncertainties relative to 1-s acquisition time and 10% of the full-scale signal are reported in Table 2. The differential measurement statistical errors in Pa and p. are propagated quadratically through Eqs. (4) by considering the enors in p' and 2 to be dependent.
We observe that the error in the absolute determination of the hemoglobin saturation Y is not much larger than the uncertainty due to the instrument noise. This fact is due to the particular dependence of Y on p' and As shown by Eq.
(4), Y depends only on the ratio jX2/pX1, and a systematic error in both and i2 has little effect on their ratio. This is particularly true in our case, since the ratio 2/1 is on the order of unity. The instrumental limit is given by the statistical errors in the third column of -10 to 100 iiM, the errors given by instrumental noise are of the order of a few percent. This is certainly a clinically acceptable uncertainty. On the other hand, the systematic errors (whose maximum estimate is reported in column 2 of Table 2), which are due to the validity of the physical model and to uneven optical coupling between LEDs and tissue, can be quite large. However, being systematic, they can be minimized by applying appropriate corrections. The in vivo results shown in Fig. 10 are reported here to support the feasibility of in vivo applications of our spectrometer. We limit the discussion of these results to two considerations. First, similar variations of hemoglobin saturation have been reported in the literature.22 Second, the absolute value of Y is an average over the tissue and is not the value relative to blood. A more complete and systematic in vivo study conducted with our tissue spectrometer is reported in a separate paper. 23

Conclusion
Since the early decades of this century, it has been proposed that the near-infrared absorption band of hemoglobin could be used to measure hemoglobin saturation directly and non- invasively.24'25 The basic idea is to exploit the differential absorption of the oxygenated and deoxygenated forms of hemoglobin in the 700-to 900-nm spectral region. Several instruments based on steady-state differential absorption have been proposed.226 Although some ofthose instruments have been fairly successful and have found regular use in clinical practice, all of them suffer from a major problem, namely, that simple differential absorption cannot compensate for the different scattering properties of the different tissues and the variability of the scattering coefficient for the same tissue among individuals. To partially overcome this intrinsic limitation of the differential absorption method, it was proposed to use more than two absorption wavelengths or the entire absorption spectrum in the 700-to 900-nm region.27 Even with this improvement, the determination of tissue oxygenation and total hemoglobin content needed some sort of a priori calibration based on empirical tables that statistically account for individual and time variability. During the 1980s a new possibility arose, due to the development of picosecond lasers with emission in the spectral region of the near-infrared hemoglobin absorption. It was shown that, by a measurement of the time of flight of a light pulse between the source fiber and the detector fiber, it was possible to determine separately the scattering and absorption coefficients of the medium.5 A new series of instruments was proposed depending on the method used to measure the time of flight. Notable are the instruments proposed by Chance et al. using the frequency domain method at a single modulation frequency.28'29 However, this method does not entirely solve the problem mentioned, since it is based on a differential phase measurement. The quantity measured by all the above instruments is always the relative oxygenation of tissues.
They cannot determine the absolute values of and p.
On the other hand, the instrument we have designed provides quantitative absolute measurements of the absorption and scattering coefficients with relatively high accuracy. It then permits one to determine the absolute values of the concentrations of oxy-and deoxyhemoglobin, and of the oxygenation in tissues. The measured quantities (ia, [HbO2I,[Hb], Y, THC) are displayed directly on a screen, providing a simultaneous real-time monitoring ofthese tissue parameters. Time derivatives and time integrals of the measured quantities can be monitored in real time as well. Hemoglobin saturation results obtained in vivo in a systematic study are presented in a separate paper.23 Our instrument can also be compact. All the required instrumentation shown in Fig.   4 can fit in a light and portable unit.
There are several characteristics of our instrument that can be changed without affecting the underlying principle ideas: . The number of light sources can be augmented or decreased according to the application. For hemoglobin saturation measurement, eight sources are adequate. However, the same multiplexing principle can be applied to a much larger number of sources for the simultaneous determination of the concentration of more chromophores, for adding another wavelength, or for imaging applications.
I We have used light-emitting diodes as the light sources.
It is possible to replace them with laser diodes, with minor modifications of the driving electronics. The ad-Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/29/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx vantage of laser diodes over LEDs is that laser diodes emit monochromatic light, provide higher intensity, and can be modulated at higher frequencies. However, for the purpose of the proof of concept of a multiplexed tissue oximeter, LEDs are adequate both in light intensity and in modulation frequency. . The value of 400 Hz for the cross-correlation frequency was selected for convenience. We have experimentally tested cross-correlation frequencies from 40 to 1500 Hz, with comparable results. The use of higher values of the cross-correlation frequency allows for a better detection of faster processes. • The light-source multiplexer was constructed using mechanical relays (see Fig. 3). However, solid-state switches can be used if multiplexing speeds faster than 2.5 ms are required. The problem in the semi-infinite geometry, where source and detector are placed on the surface of the medium, is more complicated but formally identical. Eqs. (10), (11), (12) are replaced by the following equations '5: f(r,Udc,F1a,P) = rS(j.t,p) + K, g(r,Uac,pa,11) = rSac(pa,IJ) + h(r,t,p,p) = rS(p,p) + K where f g, h are known functions of their arguments and K, are independent of r. Note that the slopes 5dc'