Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject

A 1-GHz multifrequency, multiwavelength frequency-domain photon migration instrument is used to measure quantitatively the optical absorption (cid:126)(cid:109) a (cid:33) and effective optical scattering (cid:126)(cid:109) s (cid:57)(cid:33) of normal and malignant tissues in a human subject. Large ellipsoidal (cid:126)(cid:59) 10-cm major axis, (cid:59) 6-cm minor axes (cid:33) subcutaneous malignant lesions were compared with adjacent normal sites in the abdomen and back. Absorption coefﬁcients recorded at 674, 811, 849, and 956 nm were used to calculate tissue hemoglobin concentration (cid:126) oxyhemoglobin, deoxyhemoglobin, and total (cid:33) , water concentration, hemoglobin oxygen saturation, and blood volume fraction in vivo . Our results show that the normal and the malignant tissues measured in the patient have clearly resolvable optical and physiological property differences that may be broadly useful in identifying and characterizing tumors. © 1997 Optical Society of America


Introduction
Considerable interest has been generated in the use of optical techniques for locating, identifying, and monitoring malignant transformations. Optical methods are particularly attractive because not only do they offer the possibility of providing tissue functional information, they are relatively inexpensive and do not employ ionizing radiation. However, the precise relationship between in vivo optical properties and in vivo tissue physiology is not well understood. Extensive in vitro measurements of the optical properties of various tissues have been reported in the literature 1-3 but it is not clear from these studies how the optical properties of various types of biological tissue differ from each other in vivo. Consequently our goal is to determine quantitatively absolute optical and physiological properties of human tissues in vivo and correlate this information with conventional structural data derived from other sources ͑e.g., x-ray imaging, histopathology͒. Because optical properties ͑absolute absorption and scattering parameters͒ are the fundamental determinants of contrast in optical images, we believe that quantitative in vivo measurements are essential for realistically estimating the feasibility of optical detection of tumors.
To obtain accurate quantitative measurements of the absolute optical parameters of various types of tissue, we have constructed a portable, highbandwidth ͑0.3 MHz-1 GHz͒, multiwavelength frequency-domain photon migration ͑FDPM͒ instrument. 4,5 The focus of our efforts in performing the frequency-domain measurements presented in this paper is to characterize normal and malignant tissue transformations encountered in a human subject. FDPM is an optical technique that can be used to determine quantitatively absolute tissue optical absorption and reduced scattering parameters in a single, noninvasive measurement. In FDPM the intensity of light incident upon an optically turbid sample is modulated at high frequencies, and the diffusely reflected or transmitted signal is measured with a phase-sensitive detector. Amplitudemodulated light propagates through multiplescattering media with a coherent front, forming photon density waves ͑PDW's͒. 6 -8 PDW dispersion is highly dependent on the optical properties of the medium. 9 Thus measurements of the frequency-or distance-dependent phase and amplitude of PDW's can be used to derive absolute optical absorption and reduced scattering coefficients within a turbid medium.
In this paper we concentrate on the relationship between in vivo optical properties and tissue physiological parameters in a single human subject. It is not our intent to present a library of optical properties obtained from multiple human subjects, and it is unclear whether simple cataloging will provide sufficient predictive power for identifying malignancies by the use of optical imaging methods. Rather, we present a detailed study on a single patient with multiple normal and malignant sites in order to characterize a system with built-in internal controls. In this manner, we expect to gain fundamental insight into the precise nature of optical and physiological property changes that can occur in the case of malignant transformation. By obtaining individual patient information, we hope to clarify specific detectable physiological changes that can be exploited by optical diagnostic methods. Consequently we use the absolute optical properties extracted from in vivo FDPM measurements at multiple wavelengths to calculate hemoglobin ͑Hb͒ concentration ͑oxygenated, deoxygenated, and total forms͒, blood volume fraction ͑BVF͒ in the tissue, O 2 saturation of Hb, and H 2 O concentration. Our results clearly show that tumor and normal tissue optical properties and physiological parameters measured in vivo differ substantially within the individual we studied.

Theory: Frequency-Domain Diffusion Model for a Semi-infinite Medium
Frequency-domain methods, in which the light source intensity is modulated at high frequency, have been successfully applied to in vitro spectroscopy studies of turbid media. 5,9 -12 Analytical solutions to the frequency-domain standard diffusion equation ͑SDE͒ were employed in these studies to extract accurate absolute absorption and reduced scattering coefficient spectra from frequency-domain data acquired in turbid media. The frequency-domain SDE has been estimated to be applicable to the study of thick, turbid, macroscopically homogeneous turbid media when the source-detector separation is typically greater than 1 cm and the source modulation frequency is less than 1 GHz. 13 The frequencydomain measurements presented in this paper were noninvasively performed with the light source and the light detector placed directly on the turbid medium surface in a reflection geometry under conditions in which the SDE is applicable. We have therefore employed analytical frequency-domain SDE expressions derived by Haskell et al. 14 to extract absolute absorption and reduced scattering coefficients from our frequency-domain phase-shift data. These frequency-domain SDE expressions, which take into account the index of refraction mismatch at the interface between air and the turbid medium, assume that the turbid medium under study is semiinfinite in extent and macroscopically homogeneous. The equations that describe the phase shift ⌽ of a PDW propagating in a macroscopically homogeneous semi-infinite medium ͑equations 2.7.1 and 2.7.2 in the paper by Haskell et al. 14 ͒ are given as where Here, a is the absolute absorption coefficient in units of inverse centimeters, Ј s is the reduced scattering coefficient in units of inverse centimeters, is the distance separating the source and the detector on the surface of the turbid medium in units of centimeters, is the angular intensity-modulation frequency of the light source, c is the speed of light in the transporting medium surrounding the scattering particles, and R eff is the effective reflection coefficient. R eff ͑defined in equation 2.3.7 in the paper by Haskell et al. 14 ͒ represents the fraction of the diffusing light in the semi-infinite turbid medium that is internally reflected because of the index of refraction mismatch at the medium boundary. Equations ͑1͒-͑7͒ describe an extrapolated boundary condition, which is schematically represented in Fig. 1. Z b is the distance from the medium surface to the extrapolated boundary. We calculate R eff from indices of refraction n and n out ͑see Fig. 1 for definitions͒, utilizing the Fresnel reflection coefficient for unpolarized light. 14 We use Eq. ͑1͒ to extract the absolute optical absorption coefficient a and reduced scattering coefficient Ј s from frequency-domain data acquired in vivo in biological tissue. Our goal is to calculate in vivo tissue physiological properties from in vivo measurements of a and Ј s at multiple light source wavelengths and multiple source-detector separations .

A. Portable, Multisource, High-Bandwidth Frequency-Domain Photon Migration Instrument
A portable, multilight source, high-bandwidth, FDPM instrument is used to perform all of our measurements. 5 A network analyzer ͑Hewlett-Packard Model 8753C͒ is used to produce modulation swept from 300 kHz to 1 GHz that is superimposed on the direct current of a diode laser. Four different lasers are currently available on this instrument ͑SDL, Inc. Models 7421, 5420, 5421, and 6321 at 674, 811, 849, and 956 nm, respectively͒ and each diode is addressed serially by a rf switch. The optical power coupled into the tissue on the day of our measurements on the human subject averaged approximately 30 mW for the 674-, 811-, and 849-nm laser diodes and approximately 1 mW for the 956-nm laser diode. An avalanche photodiode ͑Hamamatsu Model C5658͒ is used to detect the diffuse optical signal that propagates through the biological tissue. A 100-mdiameter gradient-index fiber is coupled to the light source used for tissue measurements, with the avalanche photodiode and the probe end of the source optical fiber in direct contact with the patient ͑i.e., a semi-infinite medium measurement geometry, Fig.  1͒. Measurement time depends on the precision required and the number of sweeps performed. For the measurements performed on the human subject, the time used to sweep over the 1-GHz band of modulation frequencies was 1 s. The network analyzer is controlled by a computer ͑Macintosh Quadra͒ and virtual instrument software ͑LABVIEW, National In-struments͒. The source-detector separations used for our FDPM measurements on the human subject were 1.7, 2.2, and 2.7 cm.

B. Calibration of the Frequency-Domain Apparatus
A measurement of the phase shift of intensitymodulated light at source wavelength propagating through a turbid medium at a given source-detector separation can be expressed as where ⌽ measured ͑ a , Ј s , , ͒ is the phase shift measured at at angular modulation frequency and source wavelength , ⌽ medium ͑ a , Ј s , , ͒ is the actual phase shift of the intensity-modulated light caused only by the medium optical properties, and ⌽ instrument ͑, ͒ is the instrument phase. ⌽ instrument ͑, ͒ is dependent on the properties of the light source, detector, optical fibers, and the electrical response of the phase-sensitive detection system. Because a ͑͒ and Ј s ͑͒ are the immediate quantities of interest in a FDPM measurement, an accurate determination of these optical parameters from the phase-shift data necessitates an analysis of ⌽ medium ͑ a , Ј s , , ͒ data rather than a direct analysis of ⌽ measured ͑ a , Ј s , , ͒ data. Thus we subtract ⌽ instrument ͑, ͒ from ⌽ measured ͑ a , Ј s , , ͒ data before the data analysis in order to yield more accurate values of a ͑͒ and Ј s ͑͒ from our FDPM data fits. One method for eliminating the instrument response from FDPM data acquired in a macroscopically homogeneous turbid medium is to compare PDW properties measured at two different sourcedetector separations, and o . Assuming that the instrument response at a given source wavelength is constant for separate measurements at and o , the behavior of the resulting FDPM data should be entirely reflective of the optical properties of the turbid medium under investigation and independent of the above-mentioned instrument response. When this two-distances measurement technique is used, Eq. ͑8͒ yields where ⌽ instrument ͑, ͒ has been eliminated from the measured data, thereby allowing SDE phase-shift equations to be applied directly to the resultant FDPM data. Accurate a ͑͒ and Ј s ͑͒ spectra have been obtained by Fishkin et al. for a macroscopically homogeneous 2.5-M methemoglobin͞1.5% Lyposyn medium; they used the frequency-domain SDE to fit FDPM data acquired with the two-distances technique. 10 Accurate absolute optical spectra of turbid media have also been acquired by Fantini et al., who used this same technique. 11 This approach works well under macroscopically homogeneous measurement conditions because the frequency-domain SDE assumes that a ͑͒ and Ј s ͑͒ are independent of the source-detector separation.
However, in human biological tissues, the assumption that the a ͑͒ and Ј s ͑͒ values are constant throughout the tissue is not necessarily valid. The  14 The placement of the image is scaled approximately for an air-medium interface, with the refractive index of the medium equal to that of tissue. 15 two-distances measurement technique may compound inaccuracies inherent in applying the SDE ͑which assumes macroscopic homogeneity͒ to macroscopically heterogeneous systems. For this reason, we determine optical properties from in vivo FDPM data acquired at a single source-detector separation . Although the application of the SDE to FDPM data acquired at a single may still not be strictly accurate, we assume that the a ͑͒ and Ј s ͑͒ values measured represent an average for the heterogeneous region probed. By using this approach, we can estimate the degree of tissue heterogeneity by evaluating the optical properties at multiple values of .
In order to extract ⌽ medium ͑ a , Ј s , , ͒ from ⌽ measured ͑ a , Ј s , , ͒ at a single source-detector separation , ⌽ instrument ͑, ͒ must be explicitly evaluated ͓see Eq. ͑8͔͒. We account for the contribution of ⌽ instrument ͑, ͒ to ⌽ measured ͑ a , Ј s , , ͒ by calibrating the FDPM instrument at each on a macroscopically homogeneous tissuelike reference material of known optical properties. The optical properties a ͑͒ ref and Ј s ͑͒ ref of the homogeneous standard are obtained from FDPM data acquired with the twodistances technique. We note from Eq. ͑8͒ that the uncertainty in ⌽ instrument ͑, ͒ must propagate into ⌽ medium ͑ a , Ј s , , ͒. The magnitude of these uncertainties has a direct impact on errors in optical and physiological property calculations.

C. Measurements on a Human Subject
We have conducted noninvasive optical property measurements of palpable tumors in a human subject. Experiments were conducted under the guidelines of the University of California at Irvine, Institutional Re-view Board-approved protocol 95-563. The patient was a 62-year-old white male with poorly differentiated, large-cell primary lung carcinoma. Three months after his initial staging workup, multiple subcutaneous masses began appearing over his trunk and extremities. Histological examination of needle biopsy specimens revealed poorly differentiated largecell adenocarcinoma, similar to the primary lung cancer.
FDPM measurements were performed on two palpable subcutaneous lesions ͑one abdominal, one back, ellipsoidal shape with ϳ10-cm major axis, ϳ6-cm minor axes͒ and compared with opposite-side normal tissue. Figure 2 shows computer-aided tomography ͑CT͒ images of the subject's trunk obtained one month before the FDPM measurements. Tumors appeared to increase in size during the time interval between CT and FDPM scans. The patient received oral and intravenous iodine-based contrast agents for this CT scan. The Fig. 2͑a͒ CT image shows the abdominal tumor measurement site, indicated by the right arrow, and the adjacent normal tissue measurement location, indicated by the left arrow. In Fig.  2͑b͒, images of the back tumor and normal measurement sites are indicated by the left and the right arrows, respectively. The CT scans clearly show that for the 1.7-2.7-cm range of source-detector separations employed, FDPM data were primarily influenced by tumor and subcutaneous fat. Although the abdominal tumor had approximately a 1-cm-thick layer of skin and fat above it, this zone is likely to have been depleted by the time FDPM measurements were performed, because of rapid tumor growth during the 1-month interval between the CT scan and the FDPM measurement. The back tumor did not appear to have an appreciable layer of normal tissue above it. Of course, CT images do not necessarily reveal the exact zone of malignant tissue. Thus it is possible that the tumor optical property measurements may, to some extent, contain a small contribution from surrounding normal structures. However, we believe that this effect is probably minimal in view of the high tumor-normal tissue optical property contrast and the good agreement between the measurements of the stomach and back malignant sites ͑see Section 4͒.
The patient was breathing O 2 from a tank ͑through a nasal cannula at 2 L͞min͒ before and throughout the duration of our FDPM measurements. All four of the diode laser sources currently available on our FDPM instrument were used in these measurements: 674, 811, 849, and 956 nm ͑average power coupled to the tissue surface was approximately 30 mW for the 674-, 811-, and 849-nm sources and approximately 1 mW for the 956-nm diode because of poor coupling of the optical fiber with the diode laser source͒. As described above, the source modulation frequencies ranged from 300 kHz to 1 GHz, and FDPM data were recorded in 5-MHz increments. Average phase shift ⌽ measured ͑ a , Ј s , , ͒ values were obtained over this ϳ1-GHz bandwidth by the performance of two multifrequency sweeps per measurement. The uncertainty in ⌽ measured ͑ a , Ј s , , ͒ is the standard deviation from this quantity ͑determined by the averaging of the deviations from this quantity over the total number of frequency sweeps͒. The uncertainty in ⌽ measured ͑ a , Ј s , , ͒ together with the uncertainty in ⌽ instrument ͑, ͒ ͑which, as we mentioned above in Subsection 3.B, is determined by making a calibration measurement on a macroscopically homogeneous standard phantom͒ determines the magnitude of the error bars on the ⌽ medium ͑ a , Ј s , , ͒ data shown in Fig. 3. A handheld probe was used that accommodated several source-detector separations, ranging from 1.2 to 2.7 cm in 0.5-cm increments. The FDPM instrument was calibrated as described above by the performance of measurements at a fixed source-detector separation on a standard reference material. Phase-shift data obtained from FDPM measurements on tissue ͓see ⌽ medium ͑ a , Ј s , , ͒ data, Fig. 3͔ were fit to Eq. ͑1͒ to extract the absolute optical absorption coefficient a and the absolute optical reduced scattering coefficient Ј s at a given and source-detector separation . Each point of the phase shift versus frequency data fit to Eq. ͑1͒ was weighted in that fit according to the magnitude of its error bar. Minimization of the 2 surface in the fitting of the phase shift versus frequency data was obtained by the use of a Marquardt-Levenberg algorithm for minimizing 2 with respect to the fitting parameters a and Ј s in Eq. ͑1͒. A tissue refractive index of 1.40 was assumed in these data fits 15 ; hence the value calculated for the effective reflection coefficient ͓see Eq. ͑7͔͒ was R eff ϭ 0.493. 14 We assume that the chomophores contributing to a in the human subject are principally oxyhemoglobin, deoxyhemoglobin, 16 and H 2 O. The concentration of each component in the tissue is determined from the FDPM measurements of a at three different wavelengths. A system of three equations of the form is solved, where ⑀ ͓chrom.͔ is the extinction coefficient ͑in units of square centimeters per mole͒ of a given chromophore at wavelength and ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ are, respectively, the concentration of Hb, oxygenated Hb, and H 2 O ͑in units of mole per cubic centimeter͒ in the tissue under study. Because measurements of a are made at four different light wavelengths, we use two different sets of three equations to determine the three unknown quantities ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔. ⑀ ͓Hb͔ , ⑀ ͓HbO 2 ͔ , and ⑀ ͓H 2 O͔ are obtained from literature values ͑note that we report these literature values in a natural logarithm scale͒. 17,18 For the wavelengths of 674, 811, and 956 nm, the matrix representation of the system of three equations given by Eq. ͑10͒ is Each column of the matrix in Eq. ͑11͒ contains the extinction coefficients of a given chromophore at each of the above-mentioned wavelengths. Each row of the matrix corresponds to a different light wavelength . Multiplication of the above equation by the inverse of the above matrix of extinction coefficients yields values for ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ in the tissue interrogated by our FPDM instrument. For the wavelengths of 674, 849, and 956 nm, the matrix representation of the system of three equations given by Eq. ͑10͒ is ͫ 6.5783 ϫ 10 6 1.8089 ϫ 10 6 1.5006 ϫ 10 6 0.7401 ϫ 10 6 2.6588 ϫ 10 6 3.0486 ϫ 10 6 0.0748 0.781 a 849 a 956 ͪ . (12) Given the comparable magnitude and relatively small values of ⑀ ͓H 2 O͔ at 811 and 849 nm ͑i.e., ⑀ ͓H 2 O͔ at 811 and 849 nm is more than a factor of 10 6 less than the Hb extinction coefficients ⑀ ͓Hb͔ and ⑀ ͓HbO 2 ͔ at 811 and 849 nm͒, we did not find it useful to use the 811and 849-nm wavelengths together in our system of three equations and three unknowns to extract absolute concentration of ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ in the tissue. Rather, we found it preferable to include the a value measured at only one or the other of these wavelengths with the 674-and 956-nm a values in our system of three equations. This allowed for the simultaneous extraction of ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ concentration from our a data. ͓Please refer to the above matrix Eqs. ͑11͒ and ͑12͒ for the ⑀ ͓H 2 O͔ values͔. Confirmation of the validity of this approach is provided by our observation that the use of either 674and 811-nm a data, or 674-and 849-nm a data in a system of ͑two equations͒͑͞two unknowns͒ yields, within experimental uncertainties, the same result for ͓Hb͔ and ͓HbO 2 ͔. We therefore stress that inclusion of the a value determined at 956 nm into our system of three equations was essential for extracting absolute H 2 O concentration from our in vivo tissue measurements.
Finally, for a system of equations of the form of Eq. ͑11͒ or Eq. ͑12͒, in which the 3 ϫ 3 matrix in these equations is given as the total uncertainties ␦ for each parameter ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ can be determined, i.e., Figure 3 compares the phase versus frequency response obtained on normal and malignant abdominal tissue. These phase-shift data were acquired at a 1.7-cm source-detector separation for four different wavelengths. Phase values have been corrected for ⌽ instrument ͑, ͒, as described above, by the use of a standard reference material. The information presented in Fig. 3 is therefore entirely a consequence of the tissue optical properties, the source modulation frequency, and the 1.7-cm source-detector separation on the tissue surface. Note that at all wavelengths and modulation frequencies, the normal abdominal tissue phase lag is greater than that of the tumor. In addition, the normal tissue phase versus frequency response displays greater curvature than the tumor phase versus frequency data. Figure 3͑d͒ data are relatively noisy because of the lower average optical power of the 956-nm diode laser ͑only 1-mW average power͒. Figure 4 shows plots of a and Ј s values extracted from best fits of the abdomen phase shift versus modulation frequency data ͑shown in Fig. 3͒ and from best fits of phase shift versus frequency data ͑not shown͒ obtained from normal and malignant tissue on the human subject's back. The fitting expression is given by Eq. ͑1͒. The uncertainties shown for the a and Ј s values were estimated for each fit from the 2 distribution by the use of a 0.67 confidence interval. Tables 1 and 2 show the optical parameters a and Ј s extracted from the fits to all the phase-shift data acquired from the human subject's abdomen and back ͑both normal and malignant tissue͒ at all source-detector separations ͑i.e., 1.7, 2.2, and 2.7 cm͒ Fig. 4. ͑a͒ Absolute absorption coefficient a versus source wavelength obtained for normal and malignant tissue on the human subject's abdomen. The a values were extracted from best fits of Eq. ͑1͒ to the abdomen phase shift versus modulation frequency data ͑shown in Fig. 3͒. The source-detector separation was 1.7 cm. ͑b͒ Reduced scattering coefficient Ј s versus source wavelength obtained for normal and malignant tissue on the human subject's abdomen. The Ј s values were extracted from best fits of Eq. ͑1͒ to the abdomen phase shift versus modulation frequency data ͑shown in Fig. 3͒. The source-detector separation was 1.7 cm. ͑c͒ Same as ͑a͒, except that the a values were obtained for normal and tumor tissue on the subject's back. The source-detector separation was 2.2 cm for these measurements. ͑d͒ Same as ͑b͒, except that the Ј s values were obtained for normal and tumor tissue on the subject's back. The source-detector separation was 2.2 cm for these measurements. and at each wavelength . These results confirm significant absorption differences between normal and tumor tissue at all wavelengths. Scattering changes are less significant, but exhibit consistent wavelength-dependent behavior. Lower tumor scattering parameters ͑versus normal tissue͒ may be due to a loss of cellularity and increased H 2 O content of necrotic zones. This could diminish both the density and the efficiency of available scatterers. Consequently we expect that Ј s measurements may be more sensitive to early-stage highly cellular tumors. Figure 5 shows quantitative bar graphs of in vivo physiological properties of the human subject's normal and malignant abdominal tissue calculated by the use of combinations of a values obtained at three different wavelengths ͓see Eqs. ͑11͒ and ͑12͔͒. The a values used to generate the numbers shown in Fig.  5 were extracted from the best fits of our phase data acquired at a 1.7-cm source-detector separation. The in vivo physiological parameters displayed in Figs. 5͑a͒ and 5͑b͒ are, respectively, deoxygenated and oxygenated Hb concentrations ͑i.e., ͓Hb͔ and ͓HbO 2 ͔, in units of millimolar concentration͒ and H 2 O concentration ͓͑H 2 O͔ in units of molar concen-tration͒. The combinations of a values used in our calculations of ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ were chosen to minimize the uncertainty in these parameters that we calculated from Eqs. ͑14͒-͑16͒. For the reasons already given above in Subsection 3.C., we did not find it useful to use the a values acquired at 811 and 849 nm together in the system of three equations given by Eq. ͑10͒. We believe that the best way to reduce the uncertainty in the H 2 O concentration extracted from our data will be to improve the precision of the a values acquired at 956 nm. Improvement in the signal-to-noise ratio of our measurements at 956 nm by an increase in the optical power coupled to the tissue should be useful in improving the precision with which we may determine a and hence absolute H 2 O concentration in future in vivo measurements. The average power of the 956-nm light coupled to the tissue in the measurements presented here can be increased from 1 to approximately 30 mW. Figure  5͑a͒ shows that both ͓Hb͔ and ͓HbO 2 ͔ ͑and hence total Hb concentration͒ in the abdominal tumor tissue were approximately double that of the normal abdominal tissue. Figure 5͑b͒ shows the abdominal tumor tissue to have a higher H 2 O concentration than the normal abdominal tissue, although it must be noted that the error on the abdominal tumor tissue H 2 O concentration is large because of the large uncertainty in a 956 used in the calculation of this quantity ͓see Fig. 4͑a͒ and the columns under Tumor Abdomen in Table 1. Although the relative values of ͓H 2 O͔ are probably correct, it is important to point out that the accuracy of the absolute ͓H 2 O͔ quantity is not easy to estimate. This is because we determined ͓H 2 O͔ from ⑀ ͓H2 O͔ values measured in pure systems. 17 Although these are probably the most accurate H 2 O extinction coefficients available, they may not be exact for biological systems in which H 2 O is found in a variety of states ͑e.g., protein bound, free͒ that can have an impact on ⑀ ͓H 2 O͔ . Table 3 shows the results of the calculation of ͓Hb͔, ͓HbO 2 ͔, and ͓H 2 O͔ by the use of a values measured at given source-detector separations on the abdomen and the back ͑both normal and malignant tis-sue͒. In cases in which the phase-shift data Fig. 5. ͑a͒ Hb concentrations ͑deoxyhemoglobin, oxyhemoglobin, and total͒ for normal and tumor locations on a human abdomen that are calculated from wavelength-dependent a values ͓refer to matrix Eqs. ͑11͒ and ͑12͒ for calculation method͔, ͑b͒ H 2 O concentrations for normal and tumor locations on human abdomen that are calculated from wavelength-dependent a values ͓refer to matrix Eqs. ͑11͒ and ͑12͒ for calculation method͔. The BVF range in the subject's normal abdominal tissue is derived from the ͓Hb total ͔ values given in Table 3 and hemotologic values obtained when blood was drawn from the subject on the day of the optical FDPM measurements. The subject's hemotologic values obtained from his drawn blood were 318 g Hb total ͑͞L of erythrocytes͒ and a hematocrit ͑red blood cell volume͞blood volume͒ of 33.6%. Given that Hb total molecular weight is 64.5 ϫ 10 3 g͞mole, 19 the concentration of Hb in the subject's whole blood was approximately ͑318 g͞L͒ ϫ 0.336͑͞64.5 ϫ 10 3 g͞mole͒ ϭ 1.66 ϫ 10 3 M Hb total on the day of the FDPM measurements. Because ͓Hb total ͔ values measured by FDPM in the subject's normal abdominal tissue ranged from 29.2 to 34.8 M, we obtain a tissue BVF of ͑29.2 to 34.8 M͒͑͞1.66 ϫ 10 3 M͒ ϫ 100 ϭ 1.8%-2.1% in the subject's normal abdominal tissue. Given that the ͓Hb total ͔ values we measured by FDPM in the subject's abdominal tumor tissue range from 87 to 102 M, we obtain a ͑87 to 102 M͒͑͞1.66 ϫ 10 3 M͒ ϭ 5.2%-6.1% BVF range in the subject's abdominal tumor tissue. This is a factor of ϳ3 greater than measured normal abdominal tissue BVF.

Results and Discussion
The H 2 O volume fraction in the subject's normal abdominal tissue is derived from the ͓H 2 O͔ values given in Table 3. Given that the molecular weight of water is 18 g͞mole and the density of water is 1000 g͞L, the concentration of water is approximately ͑1000 g͞L͒͑͞18 g͞mole͒ ϭ 55.6 M. The ͓H 2 O͔ values we measured by FDPM in the subject's normal abdominal tissue range from 3.95 to 5.87 M; hence we obtain a H 2 O volume fraction range of ͑3.95 to 5.87 M͒͑͞55.6 M͒ ϫ 100 ϭ 7.1%-10.6% in the subject's normal abdominal tissue. This is comparable with the lower end of the 11.4%-30.5% range given in the literature for H 2 O percentage in human fatty adipose tissue. 20 Abdominal tumor tissue H 2 O percentage ranged from 16% to 56%, or roughly twofold-fivefold higher than that of normal abdominal tissue.
These values neglect the possibility that fat absorption contributes to a 956 . In practical terms, fat absorption is difficult to quantify and is, at the wavelengths used in this study, less significant than other tissue components. Nevertheless, H 2 O concentration measurements of normal, adiposedominated abdominal and back tissues may be artificially elevated because of an underestimation on our part of fat absorption to our measured values of a 956 . Of course, if this were the case, it would provide even further evidence of contrast between normal and malignant tissues. In any event, H 2 O contrast is likely to be primarily a reflection of differences in tumor versus normal tissue vascularity ͑i.e., BVF͒ rather than intrinsic variations in tissue H 2 O content. Other possible sources of H 2 O concentra-tion variations include increased fluid retention as indicated by elevated tumor interstitial fluid pressure levels. 21

Conclusion
Overall, optical property data from normal and malignant sites are remarkably consistent. FDPM measurements sample a combination of necrotic core and high blood volume cortex tumor regions. Regardless of the precise locations probed, we have observed that total Hb ͑which is proportional to blood volume͒ and H 2 O content are of the order of twofoldfivefold higher in tumor versus normal tissue. Scattering spectra suggest smaller, but detectable, differences in wavelength-dependent behavior between tissue types. Although these preliminary data were not recorded from breast tissues, we believe that these definitive results obtained from adenocarcinoma lesions growing in host adipose tissue ͑i.e., comparable with breast disease͒ suggest that FDPM will have utility in breast cancer diagnostics.