Noninvasive Investigation of Blood Oxygenation Dynamics of Tumors by Near-Infrared Spectroscopy

Noninvasive investigation of blood oxygenation dynamics of tumors by near-infrared spectroscopy

Hanli Liu, Yulin Song, Katherine L. Worden, Xin Jiang, Anca Constantinescu, and Ralph P. Mason

The measurement of dynamic changes in the blood oxygenation of tumor vasculature could be valuable for tumor prognosis and optimizing tumor treatment plans. In this study we employed near-infrared spectroscopy ͑NIRS͒ to measure changes in the total hemoglobin concentration together with the degree of hemoglobin oxygenation in the vascular bed of breast and prostate tumors implanted in rats. Mea- ͑ surements were made while inhaled gas was alternated between 33% oxygen and carbogen 95% O2,5% ͒ CO2 . Significant dynamic changes in tumor oxygenation were observed to accompany respiratory challenge, and these changes could be modeled with two exponential components, yielding two time constants. Following the Fick principle, we derived a simplified model to relate the time constants to tumor blood-perfusion rates. This study demonstrates that the NIRS technology can provide an efficient, real-time, noninvasive means of monitoring the vascular oxygenation dynamics of tumors and facilitate investigations of tumor vascular perfusion. This may have prognostic value and promises insight into tumor vascular development. © 2000 Optical Society of America OCIS codes: 170.1470, 170.3660, 170.4580, 170.5280, 290.1990, 290.7050.

1. Introduction Comparing needle-based, oxygen-sensitive electrodes The presence and the significance of tumor hypoxia or electron paramagnetic resonance and MRI for have been recognized since the 1950’s. There is in- measuring pO2 shows that the latter two offer the creasing evidence that tumor oxygenation is clini- advantage of facilitating multiple repeated measure- cally important in predicting tumor response to ments to map pO2 noninvasively. However, mag- radiation, tumor response to chemotherapy, overall nets are large, and the methods are not readily prognosis, or all three. Hypoxic cells in vitro and in portable. A versatile method for monitoring intra- animal tumors in vivo are documented to be 3 times tumor oxygenation rapidly and noninvasively is more resistant to radiation-induced killing compared therefore very desirable for tumor prognosis and tu- with aerobic cells.1 Recent studies show that hy- mor treatment planning. poxia may have a profound impact on malignant pro- In the near-infrared ͑NIR͒ region ͑700–900 nm͒ gression and on responsiveness to therapy.2,3 the major chromophores in tissue are oxygenated he- ͑ ͒ moglobin and deoxygenated hemoglobin, which differ Numerous studies on tumor oxygen tension pO2 measurements have been conducted in recent years in their light absorption. Measurements of the ab- by use of a variety of methods, such as microelec- sorption of light travelling through the tissue under trodes,2 phosphors,4 electron paramagnetic reso- study allow us to evaluate or quantify blood oxygen- nance,5 or magnetic resonance imaging6 ͑MRI͒. ation, such as the concentrations of oxygenated he- ͑ ͒ ͑ ͒ moglobin HbO2 , and deoxygenated hemoglobin Hb and the hemoglobin saturation SO2. In the past de- H. Liu ͑[email protected]͒, Y. Song, L. Worden, and X. Jiang are cade, three forms of NIR spectroscopy ͑NIRS͒ that with the Joint Graduate Program in Biomedical Engineering, Uni- use pulsed-laser light in the time domain, amplitude- versity of Texas at Arlington, Arlington, Texas 76109. A. Con- modulated laser light in the frequency domain, and stantinescu and R. P. Mason are with the Department of cw light in a dc form were developed for blood oxy- Radiology, University of Texas Southwestern Medical Center, Dal- 7 las, Texas 75390. genation quantification in tissue. Significant in- Received 16 March 2000; revised manuscript received 25 June vestigations in both laboratory and clinical settings 2000. by use of NIRS were conducted for noninvasive, quan- 0003-6935͞00͞285231-13$15.00͞0 titative measurements and imaging of cerebral © 2000 Optical Society of America oxygenation8–12 and blood oxygenation of exercised

1 October 2000 ͞ Vol. 39, No. 28 ͞ APPLIED OPTICS 5231 muscle13–17 in vivo. Although NIR techniques were ies and to relate the time constants to tumor blood used extensively in conjunction with cryospectropho- perfusion. Finally, in Section 5, we discuss the re- tometry to investigate tumor blood-vessel oxygen- sults, the future extensions, and the potential uses of ation in biopsies,18 only a few reports19–22 were the NIR technique as a novel diagnostic–prognostic published on using the NIR techniques for monitor- tool for tumor therapy and cancer research. ing tumor oxygenation in vivo. In principle, the the- oretical model, i.e., the diffusion approximation to the 2. Materials and Methods photon transport theory, works well for only large and homogeneous media.23,24 Accurate quantifica- A. Animal Model and Measurement Geometry tion of tumor oxygenation by use of the NIR approach NF13762 breast tumor was implanted in adult fe- is limited because of the considerable heterogeneity male Fisher rats, and Dunning prostate adenocarci- and the finite sizes of tumors. noma R3327-AT1 was implanted in adult male It is understood and documented25 that the NIR Copenhagen rats. The tumors were grown in technique used for blood oxygenation monitoring is pedicles27 on the forebacks of the rats until the tu- sensitive to vascular absorption in the measured or- mors were approximately 1–2 cm in diameter. Rats gan. The NIR method is not limited to measure- were anesthetized with 200-␮l ketamine hydrochlo- ments of blood oxygenation in arteries ͑c.f., pulse ride ͑100 mg͞ml͒ and maintained under general gas- ͑ 3͞ oximetry͒ or in veins but interrogates blood in the eous anesthesia with 33% inhaled O2 0.3 dm min 3͞ ͒ entire vascular compartment, including capillaries, O2, 0.6 dm min N2O, and 0.5% methoxyflurane arterioles, and venules, i.e., the vascular bed. A va- through a mask placed over the mouth and nose. riety of terms like cerebral oxygenation, tissue hemo- Tumors were shaved to improve the optical contact globin oxygenation, and mean hemoglobin for transmitting light. Body temperature was main- oxygenation are used in the literature7,24,26 to indi- tained with a warm-water blanket. In some cases, a cate this concept. Although tissue hemoglobin oxy- fiber-optic pulse oximeter ͑Nonin, Inc., Model 8600V͒ genation is not rigorous because hemoglobin that was manufacturer calibrated was placed on the molecules are located in only blood, the term is used hind foot to monitor arterial oxygenation SaO2, and a specifically to differentiate between the hemoglobin fiber-optic probe was inserted rectally to measure saturation in the tissue vascular bed, as measured by temperature. The tumor volume V ͑in centimeters the NIR method, and the arterial hemoglobin satu- cubed͒ was estimated as V ϭ͑4␲͞3͓͒͑L ϩ W ϩ H͒͞ ͔3 ration SaO2, as measured by a pulse oximeter. 6 , where L, W, and H are the three respective or- The goal of this paper is to demonstrate the NIR thogonal dimensions. technique as a real-time, noninvasive means of mon- Most measurements were performed with 33% oxy- itoring hemoglobin oxygenation dynamics, i.e., gen as inhaled gas to achieve a stable baseline for a changes in the concentrations of total hemoglobin period of 5 to 15 min. The inhaled gas was then ͑ ͒ ͑ ͒ ͑ Hbt and oxygenated hemoglobin HbO2 , in the vas- switched to carbogen 95% oxygen, 5% carbon diox- cular bed of breast and prostate rat tumors in re- ide͒ for at least 20 min and then switched back to 33% sponse to respiratory challenge. Compared with O2 for approximately 15 min. The complete cycle previous NIR studies of tumors in vivo, our approach lasted 1 hour. Sometimes repeated carbogen inter- has the following features: ͑1͒ The transmission ventions were performed sequentially to evaluate the mode, as opposed to the reflectance mode used by reproducibility of the time profiles of the tumors. In Hull et al.,22 interrogates deeper regions ͑central certain cases alternative gases were used, as defined parts͒ of the tumor. ͑2͒ Only two wavelengths, as in the results and figures, and some rats were sacri- opposed to the spectrum of 300–1100 nm used by ficed by KCl-induced cardiac arrest. Steen et al.,21 are employed and provide a fast and Figure 1 shows the measurement geometry: Hor- low-cost instrument. ͑3͒ A source–detector separa- izontally, the delivering and the detecting fiber bun- tion of 1–2 cm interrogates a large tumor noninva- dles were face to face in the transmittance mode, and sively, as opposed to the needlelike probe used by both were in contact with the tumor surface without Steinberg et al.20 More innovatively, on the basis of hard compression. The separation of the two bundle the experimental observation of tumor hemoglobin surfaces was between 1.0 and 2.5 cm, depending on oxygenation dynamics, we developed a tumor he- the tumor size. Vertically, the two bundle tips ͑with moperfusion model that provides important insight diameters of 0.5 cm͒ were placed around the middle of into tumor blood perfusion. the tumor. Thus the current setup of the probes This paper is organized as follows: In Section 2, provides an optimal geometry for the NIR light to we describe our animal model, the NIR instrument, interrogate deep tumor tissue with minimal interfer- and the algorithm for calculations of tumor blood ence from the foreback of the rat. oxygenation. In Section 3, we show experimental results measured from both breast and prostate tu- B. Near-Infrared Instrument and Data Analysis mors under respiratory interventions and calculate As shown in Fig. 1, we used a homodyne frequency- time constants for the hemoglobin oxygenation dy- domain photon-migration system28,29 that was capa- namics of the tumors. In Section 4, we develop a ble of determining the amplitude and the phase tumor hemoperfusion model to interpret the experi- changes of amplitude-modulated light passing mental data obtained in the tumor-intervention stud- through tumors. In this setup a rf source modulates

5232 APPLIED OPTICS ͞ Vol. 39, No. 28 ͞ 1 October 2000 Fig. 1. Experimental setup of a one-channel, NIR, frequency-domain IQ instrument for tumor oxygenation measurement. PMT, photomultiplier tube for detecting light; IQ, in-phase and quadrature demodulator for retrieving amplitude and phase information; Low Pass, low-pass filter. The 5-mm-diameter fiber bundles deliver and detect the laser light through the tumor in transmittance geometry. the light from two laser diodes ͑wavelengths of 758 with the NIR data. The experimental uncertainties and 782 nm͒ at 140 MHz. The laser light passes for arterial saturation and changes in hemoglobin con- through a combined fiber-optic bundle, is transmitted centrations were calculated by use of the baseline data through the tumor tissue, and is collected by a second taken over 5–10 min without respiratory perturbation fiber bundle. The light is then detected by a photo- to the rat. Nonlinear curve fitting based on the Mar- multiplier tube and demodulated with a commer- quardt algorithm30,31 was performed by use of Kalei- cially available in-phase and quadrature ͑IQ͒ daGraph.32 The software also provided the errors ͑or demodulator chip into its I and Q components. After uncertainties͒ for each fitted parameter, the optimized these components are put through a low-pass filter ␹2 values, and the fitting correlation coefficient R, to- they can be used to calculate the amplitude and the gether with the goodness of the fit R2.33 The signifi- phase changes caused by the tumor. These steps are cance of changes was assessed on the basis of Fisher expressed mathematically by protected-least-significant-difference analysis of vari- ance by use of Statview software. I͑t͒ ϭ 2A sin͑␻t ϩ ␪͒sin͑␻t͒ low C. Calculation for Changes in the Hemoglobin ϭ ͑␪͒ Ϫ ͑␻ ϩ ␪͒ O¡ A cos A cos t Idc Concentration pass It is well known that the NIRS of tissue can be used ϭ A cos͑␪͒, (1) to determine the total hemoglobin concentration Hbt ͑ ͒ ϭ ͑␻ ϩ ␪͒ ͑␻ ͒ and the hemoglobin oxygen saturation SO2 of an or- Q t 2A sin t cos t gan in vivo.7 When two NIR wavelengths are used low ͑758 and 782 nm, in this case͒ it is assumed that ϭ A sin͑␪͒ ϩ A sin͑␻t ϩ ␪͒ O¡ Q dc tissue background absorbance is negligible and that pass the major chromophores in organs are oxygenated ϭ A sin͑␪͒, (2) and deoxygenated hemoglobin molecules. In principle, because the IQ system can give both phase and ␪ ϭ Ϫ1͑ ͞ ͒ tan Qdc Idc , (3) amplitude values, we should be able to obtain abso- 7,28 ϭ ͑ 2 ϩ 2͒1͞2 lute calculations of HbO2, Hb, and SO2. How- A Idc Qdc , (4) ever, given the tumor’s small size and large spatial where A and ␪ are the amplitude and the phase of the heterogeneity, it is very difficult to obtain such ab- detected light, respectively, and ␻ is the angular mod- solute quantification accurately with conventional ulation frequency ͑ϭ2␲ϫ140 MHz͒. algorithms34 that are based on the diffusion approx- The two laser lights were time shared, and the con- imation. Instead, on the basis of the modified Beer– trolling process and the data acquisition both inter- Lambert law, we can use the amplitude of the light faced through a 12-bit analog-to-digital board ͑Real transmitted through the tumor to calculate concen- ͑ Time Devices, Inc., Model AD2100͒ with a maximum tration changes in HbO2, Hb, and Hbt expressed as ⌬ ⌬ ⌬ ͒ sampling rate of 4 Hz.28 However, slower sampling HbO2, Hb, Hbt, respectively of the tumor that rates were used in measurements to compensate for are caused by respiratory intervention. These experimental noise. Simple time averaging among a changes can be derived25 and expressed as ͑see Ap- few adjacent data points was performed during data pendix A for derivations and justifications͒ analysis to further decrease the noise. However, data ͑ ͒ smoothing was not applied for 1 calculating the ex- ⌬ ϭ ͑ ͒ Ϫ ͑ ͒ perimental uncertainty ͑error bars͒ or ͑2͒ fitting the Hb Hb transient Hb baseline ␭2 ␭1 time constants to prevent the fast-changing compo- ␭ Ab ␭ Ab ⑀ 1 logͩ ͪ Ϫ ⑀ 2 logͩ ͪ nent from being oversmoothed and overlooked. The HbO2 HbO2 At At pulse-oximeter data were not averaged because they ϭ ␭ ␭ ␭ ␭ , (5) ͑⑀ 2 ⑀ 1 Ϫ ⑀ 1 ⑀ 2 ͒ were recorded manually and appear discrete compared L Hb HbO2 Hb HbO2

1 October 2000 ͞ Vol. 39, No. 28 ͞ APPLIED OPTICS 5233 ⌬HbO2 ϭ HbO2͑transient͒ Ϫ HbO2͑baseline͒

␭1 ␭2 ␭ Ab ␭ Ab ⑀ 2 logͩ ͪ Ϫ ⑀ 1 logͩ ͪ Hb Hb At At ϭ ␭ ␭ ␭ ␭ , (6) ͑⑀ 2 ⑀ 1 Ϫ⑀ 1 ⑀ 2 ͒ L Hb HbO2 Hb HbO2 ␭ ␭ where ⑀ and ⑀ are extinction coefficients35 of Hb HbO2 deoxygenated and oxygenated hemoglobin, respec- ␭ tively, at wavelength ; the variable Ab is a constant amplitude of baseline; At is the transient amplitude under measurement; and L is the optical path length between the source and the detector. Using the approach suggested by Cope and Delpy,10 we can express L as L ϭ DPF ϫ d, where d is the direct source–detector separation in centime- Fig. 2. Results of a drift test of the NIR instrument by use of a ters and DPF is the ratio between the optical path tissue phantom. The thicker solid curve represents relative ⌬ length and the physical separation and is tissue de- changes in the oxygenated hemoglobin concentration, i.e., HbO2, pendent. The DPF for tumors has not been well and the thinner solid curve represents relative changes in the total ⌬ ⌬ ⌬ hemoglobin concentration, i.e., Hbt. HbO2 and Hbt were cal- studied; for simplicity, we assume the DPF to be 1 in ͑ ͒ ͑ ͒ our calculations. The justification for this simplifi- culated by use of Eqs. 8 and 9 , respectively. cation is given in Section 5. After substituting the extinction coefficients35 at 758 and 782 nm in Eqs. ͑5͒ ͑ ͒ ͑ ͒ and ͑6͒ with values of ⑀758 ϭ 0.359, ⑀758 ϭ 0.1496, ⑀782 centrations, as calculated from Eqs. 8 and 9 .In Hb HbO2 Hb ϭ 0.265 and ⑀782 ϭ 0.178, respectively, in units of this example, the standard deviations over the entire HbO2 inverse millimoles times inverse centimeters, we ar- period of 100 min were less than 0.007 and 0.004 mM, ⌬ ⌬ rive at respectively, for HbO2 and Hbt. Furthermore, we calculated uncertainties for both of these quantities 758 782 ͓7.34 log͑Ab͞At͒ Ϫ 6.17 log͑Ab͞At͒ ͔ on the basis of the propagation of errors, and the ⌬Hb ϭ , results are consistent with those shown in Fig. 2. L (7) B. Breast Tumors Figure 3͑a͒ shows the results taken from a breast 3 ⌬HbO2 ϭ tumor ͑4.5 cm ͒ with a source–detector separation of 758 782 1.8 cm. The data were smoothed, and the measure- ͓Ϫ10.92 log͑A ͞A ͒ ϩ 14.80 log͑A ͞A ͒ ͔ b t b t , ment uncertainties are shown at only discrete loca- L tions. The figure shows the relative changes in total ⌬ hemoglobin concentration Hbt and oxygenated he- (8) ⌬ moglobin concentration HbO2. The arterial Hb ⌬Hb ϭ ⌬͑HbO ϩ Hb͒ saturation was also obtained to show a relatively t 2 rapid change in arterial signals when the inhaled gas ͓Ϫ ͑ ͞ ͒758 ϩ ͑ ͞ ͒782͔ 3.58 log Ab At 8.63 log Ab At was switched from 33% O2 to carbogen. Respiratory ϭ , ⌬ ͑ Ͻ L challenge caused a sharp rise in HbO2 p 0.01 after 1 min, p Ͻ 0.0001 by 1.5 min͒ that was followed (9) by a further slow, gradual, but significant, increase ͑ Ͻ ͒ ⌬ where the units are in millimoles. Equations ͑7͒ over the next 25 min p 0.001 . Hbt also changed and ͑8͒ permit the calculation of changes in Hb and significantly ͑p Ͻ 0.001͒ within the first minute, but HbO that are due to respiratory challenge, respec- the total change was only approximately 10% of that 2 ⌬ tively, whereas Eq. ͑9͒ quantifies a relative increase of HbO2. Given the exponential appearance of the ⌬ in the total hemoglobin concentration that is caused rising part of HbO2, we used single-exponential and by the intervention. The last quantity also reflects a double-exponential expressions to fit the data in the change in blood volume because it is proportional to rising portion to better understand and quantify the ⌬ the total Hb concentration. dynamic features of HbO2. The unsmoothed data and the fitted curves are shown in Figure 3͑b͒. The 3. Results double exponential appears to give a much better fit, as is confirmed by the respective R values ͑0.98 ver- A. Instrument Drift Tests sus 0.81͒. Time constants of 0.18 Ϯ 0.02 min and The stability of the NIR instrument was tested in 27.8 Ϯ 3.9 min were obtained for fast and slow dy- terms of baseline drift after a warm-up period of namic changes, respectively, in the tumor HbO2 con- 30 min by use of a tissue phantom25,36 with stable centration. optical properties. Figure 2 shows an example of Figure 4͑a͒ was obtained from a second breast tu- a phantom measurement that displays the variation mor ͑5.9 cm3͒ with a source–detector separation of ⌬ of relative changes in apparent HbO2 and Hbt con- 1.6 cm. Here HbO2 increased rapidly after the ini-

5234 APPLIED OPTICS ͞ Vol. 39, No. 28 ͞ 1 October 2000 Fig. 3. ͑a͒ Results obtained with the NIR instrument from a 4.5-cm3 rat breast tumor while the breathing gas was switched Fig. 4. ͑a͒ Results obtained with the NIR instrument from a 3 from 33% O2 to carbogen. The thicker solid curve represents 5.9-cm rat breast tumor while the breathing gas was switched ⌬ ⌬ ͑ ͒ HbO2, the thinner solid curve represents Hbt, and the dashed from 33% O2 to carbogen. b The solid curves show the best fits ͑ ͒ curve with the filled circles represents arterial saturation. b to the HbO2 data at the rising portion. In this case a double The unsmoothed data and the fitted curves: The solid curves exponential with values of 0.09͕1 Ϫ exp͓Ϫ͑t Ϫ 9.8͒͞0.8͔͖ ϩ ⌬ represent the best fits to the HbO2 data at the rising portion. 0.16͕1 Ϫ exp͓Ϫ͑t Ϫ 9.8͒͞3.0͔͖, with R ϭ 0.98, and a single expo- The best fit to the two exponential terms is 0.143͕1 Ϫ exp͓Ϫ͑t Ϫ nential with a value of 0.250͕1 Ϫ exp͓Ϫ͑t Ϫ 9.8͒͞2.00͔͖, with R ϭ 12.5͒͞0.18͔͖ ϩ 0.36͕1 Ϫ exp͓Ϫ͑t Ϫ 12.5͒͞27.8͔͖, with R ϭ 0.98, 0.97, provided similarly good fits. whereas the best fit with one exponential term is expressed as 0.322͕1 Ϫ exp͓Ϫ͑t Ϫ 12.5͒͞5.1͔͖, with R ϭ 0.81. namic pattern, i.e., a rapid rise followed by a slow continuation. Figures 5͑b͒ and 5͑c͒ show the un- tial gas switch but did not exhibit the continued slow smoothed data together with the fitted curves for the ⌬ rise afterward. Hbt was found to increase with car- rising portions of the two repeated increases in ⌬ bogen inhalation, although the magnitude was HbO2. Again, the double-exponential expression ⌬ smaller than that of HbO2 during the period of the with two time constants produced much better fits ⌬ intervention. Again, changes in HbO2 were mod- than did the single-exponential term in both pro- ␶ ͑ ͒ eled by a single-exponential term that yielded a time cesses with two averaged time constants of 1 mean Ϯ ͑ ϭ ͒ ϭ Ϯ ␶ ͑ ͒ϭ Ϯ constant of 2.00 0.04 min R 0.97 and by a 0.26 0.11 min and 2 mean 8.2 1.8 min. double-exponential formula with two time constants Individual, respective time constants and coefficients of 0.8 Ϯ 0.2 min and 3.0 Ϯ 0.3 min ͑R ϭ 0.98͒.In are summarized in Table 1. Furthermore, single- this case both expressions fit the data well, as shown exponential and double-exponential expressions were in Fig. 4͑b͒. fitted to obtain time constants for the decay processes To demonstrate the reproducibility of the dynamic after the inhaled gas was switched repeatedly back to changes in response to respiratory challenge, we sub- the baseline conditions. Similarly, the double- jected one animal to repeat carbogen inhalation. exponential expression fits the data better with two ͑ ͒ ␶ decay ͑ ͒ϭ Ϯ Figure 5 a shows measurements taken from a breast mean time constants of 1 mean 0.17 0.07 ͑ 3͒ ␶ decay ͑ ͒ϭ Ϯ tumor 6.7 cm with a source–detector separation of min and 2 mean 12.2 0.7 min for the two 2 cm. In this case air with 1.2% isoflurane ͑anes- decay processes. ͒ thetic was used as the baseline instead of 33% O2. To further validate our experimental observations, This figure shows a very consistent pattern in two we subjected some rats to cardiac arrest ͑with KCl͒ to repeated time responses with a fast and a slow in- observe the changes in HbO2 and Hbt on death. Fig- ⌬ ⌬ crease in HbO2. Here Hbt shows a similar dy- ure 6 shows an example of cardiac arrest on a rat with

1 October 2000 ͞ Vol. 39, No. 28 ͞ APPLIED OPTICS 5235 2 2 R HbO ⌬ ␶͔͒ ͒ ͞ t 0.005 0.66 0.001 0.94 0.001 0.80 0.001 0.66 0.001 0.67 0.02 0.94 mM ͑Ϫ Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ͑ A exp Ϫ 1 ͓ 1 A ͒ 0.04 0.250 0.3 0.322 0.03 0.550 0.02 0.485 0.02 0.140 1.6 0.37 ϭ Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ min ␶͑ Single-Exponential Fitting 2 2 A ␶ ͞ ͞ 0.01 5.1 0.01 2.80 0.18 2.00 0.01 1.38 0.01 1.13 1.2 14.8 1 1 ␶ A Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ϭ 1 2 f f 1 2 ͔͒ 2 A A ␶ 0.03 61.35 0.14 2.11 0.01 24.27 0.01 39.30 0.03 31.95 0.03 0.6 ͞ t Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ϭ ͑Ϫ 1 2 ␥ ␥ exp Ϫ 1 ͓ 2 0.001 0.40 0.001 0.63 0.07 0.56 0.001 1.38 0.001 1.41 2 0.20 0.01 A ␶ ͞ Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ 1 ␶ ͔͒ ϩ 2 ␶ ͞ t ͑Ϫ 2 R exp Ϫ 1 ͓ ͒ 1 0.002 0.97 0.026 0.03 0.96 0.006 0.02 0.96 0.27 0.001 0.99 0.035 0.001 0.93 0.044 0.03 0.94 0.02 A mM Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ͑ ϭ 2 2 A HbO ⌬ ͒ 0.003 0.36 0.002 0.368 0.02 0.16 0.001 0.233 0.001 0.064 0.01 0.38 mM Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ͑ 1 A Table 1. Summary of the Vascular Oxygen Dynamics ͒ 3.9 0.143 0.09 0.232 0.3 0.09 0.12 0.321 0.15 0.090 3.1 0.004 min Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ͑ 2 ͒␶ 0.01 6.93 0.003 9.47 0.02 27.8 0.2 3.0 0.007 6.02 4.5 15.6 min Ϯ Ϯ Ϯ Ϯ Ϯ Ϯ ͑ 1 ͒␶ 3 Fig. 5. ͑a͒ Relative changes in the HbO detected with the NIR 2 cm instrument from a rat breast tumor ͑6.7 cm3͒ while the breathing ͑ 4.5 1.8 5.96.7 0.8 0.18 6.7 0.332 8.2 0.265

͑ ͒ 10.8 0.3 gas was alternated between air 21% O2 and carbogen. The best fits to the HbO2 data by use of both the double-exponential and the single-exponential expressions for ͑b͒ the first and ͑c͒ the second ͒ ͒ ͒ respiratory challenges are shown. The fitted equations that were ͒ ͒

obtained from ͑b͒ are 0.232͕1 Ϫ exp͓Ϫ͑t Ϫ 19.5͒͞0.18͔͖ ϩ 0.368͕1 Ϫ Tumor Double-Exponential Fitting Fig. 7 Fig. 8 ͑ exp͓Ϫ͑t Ϫ 19.5͒͞6.93͔͖, with R ϭ 0.98, and 0.550͕1 Ϫ exp͓Ϫ͑t Ϫ ͑ Fig. 3 Fig. 4 Fig. 5 ͑ 19.5͒͞2.80͔͖, with R ϭ 0.89, respectively. The ﬁtted equations ͑ ͑ Type Volume that were obtained from ͑c͒ were 0.321͕1 Ϫ exp͓Ϫ͑t Ϫ 67͒͞0.332͔͖ ϩ 0.233͕1 Ϫ exp͓Ϫ͑t Ϫ 67͒͞9.47͔͖, with R ϭ 0.99, and 0.485͕1 Ϫ Breast Breast Breast Prostate exp͓Ϫ͑t Ϫ 67͒͞1.38͔͖, with R ϭ 0.81, respectively. Prostate

5236 APPLIED OPTICS ͞ Vol. 39, No. 28 ͞ 1 October 2000 Fig. 6. Inﬂuence of KCl-induced cardiac arrest on the values of ͑ 3͒ HbO2 and Hbt of a breast tumor 5.3 cm , while the rat was breathing air.

͑ 3͒ ⌬ ⌬ a breast tumor 5.3 cm . Both Hbt and HbO2 dropped signiﬁcantly, immediately after KCL was ⌬ admitted intravenously. Within 1 min Hbt ⌬ reached a plateau, whereas HbO2 decreased rapidly within the ﬁrst 30 s and then was followed by a slow prolongation.

C. Prostate Tumors Figure 7͑a͒ was obtained from a large prostate tumor ͑ ͒ ͑ 3 Fig. 7. a Influence of respiratory challenges switching from air ͑8.2 cm ͒. In common with the breast tumors, ͒ to carbogen on the values of HbO2 and Hbt of a large rat prostate ⌬ 3 HbO2 showed a rapid initial increase that was fol- tumor ͑8.2 cm ͒. ͑b͒ The best-fitted equations are 0.090͕1 Ϫ ⌬ lowed by a slower continuation. Hbt increased rap- exp͓Ϫ͑t Ϫ 12͒͞0.265͔͖ ϩ 0.064͕1 Ϫ exp͓Ϫ͑t Ϫ 12͒͞6.02͔͖, with R ϭ idly and then reached a plateau. Figure 7͑b͒ shows 0.96, and 0.140͕1 Ϫ exp͓Ϫ͑t Ϫ 12͒͞1.13͔͖, with R ϭ 0.82, for the that the double-exponential equation fits the un- double-exponential and the single-exponential expressions, respec- smoothed data better ͑R ϭ 0.96͒ than does the single- tively. exponential term ͑R ϭ 0.82͒. Here the fast and the slow time constants are 0.265 Ϯ 0.007 min and 6.02 Ϯ 0.15 min, respectively. expression with a fast and a slow time constant than Figure 8͑a͒ was obtained from another large pros- they were by a single-exponential fitting. Dynamic tate tumor ͑10.8 cm3 with a source–detector separa- changes in arterial saturation preceded those in ͒ ⌬ tion of 2.5 cm . Here HbO2 displayed a gradual HbO2. The detailed parameters regarding tumor increase throughout the entire period of carbogen in- size, fitted time constants, corresponding magni- ⌬ 2 halation, whereas the increase in Hbt was consid- tudes, and R are listed in Table 1. erably delayed. Variations in arterial hemoglobin 4. Model for the Blood Oxygenation Dynamics of saturation SaO2 are also shown and were very rapid ⌬ Tumors in comparison with HbO2, in common with Fig. 3. ⌬ HbO2 dropped rapidly when the inhaled gas was As was shown in Section 3, the temporal changes in switched back from carbogen to 33% O2. Both the HbO2 caused by respiratory challenge can be fitted single-exponential and the double-exponential ex- with an exponential equation that has either one or pressions were used to obtain time constants for the two time constants ͑fast and slow͒. In this section, ⌬ rising portion of HbO2 that was due to carbogen we further derive and simplify a hemoperfusion intervention. In this case both expressions gave model to interpret these time constants and to corre- equally good fits, as shown in Fig. 8͑b͒ and Table 1. late the experimental findings with the physiology of ␶ decay ϭ Ϯ For the decay process, we obtained 1 0.6 0.2 the tumors. ␶ decay ϭ Ϯ ϭ min and 2 6.6 1.7 min with R 0.94 for the To develop the model, we follow an approach used double-exponential fitting, whereas the single- to measure regional cerebral blood flow ͑rCBF͒ with exponential fitting resulted in ␶ϭ2.8 Ϯ 0.4 min with diffusible radiotracers, as originally developed by R ϭ 0.88. For comparison the rat was also chal- Kety37 in the 1950’s. The basic model was modified lenged with 100% O2. in a variety of ways to adapt it to positron emission In summary, we observed dynamic changes in tomography studies.38,39 By analogy, we can evalu- HbO2 that were due to carbogen intervention for both ate tumor hemodynamics such as tumor blood flow breast and prostate tumors. In most cases these ͑perfusion͒ by using the respiratory-intervention gas changes were modeled better by a double-exponential as a tracer.

1 October 2000 ͞ Vol. 39, No. 28 ͞ APPLIED OPTICS 5237 ͑ ͒ ␭ In Eq. 10b , f and are constants, whereas Ct is a ͑ ͒ time-dependent variable that is written as Ct t .In principle, the arterial-tracer concentration Ca is a time-varying quantity. If a certain concentration of the arterial tracer is administrated continuously starting at time 0, Ca can be expressed mathemati- ͑ ͒ cally as a constant value of Ca 0 after time 0. Then Eq. ͑10b͒ can be solved as

Ct͑t͒ ϭ ␭Ca͑0͓͒1 Ϫ exp͑Ϫft͞␭͔͒. (11) Equation ͑11͒ indicates that, at time t after the onset of tracer administration, the local tissue ͑traditional- ͒ ͑ ͒ ly brain Ct t concentration depends on the blood ͑ ͒ ﬂow f, the arterial time–activity curve Ca 0 , and the partition coefﬁcient ␭. In response to respiratory intervention, a sudden small change is introduced into the arterial O2 saturation SaO2, and the resulting increase in arterial ͑⌬ artery͒ HbO2 concentration HbO2 can be considered as an intravascular tracer.40 Following Kety’s method and assuming that changes in dissolved O2 are negligible,40 we have

d ͑⌬HbO vasculature͒ ϭ dt 2 ⌬HbO vasculature fͩ⌬HbO artery Ϫ 2 ͪ . 2 ␥

(12) Fig. 8. ͑a͒ Variations in S O , ⌬HbO , and Hb of which the latter a 2 2 t ͑ ͒ two were detected with the NIR instrument, from a large rat where f still represents blood flow or perfusion rate prostate tumor ͑10.8 cm3͒ during respiratory challenge. ͑b͒ The and ␥ is defined as a vasculature coefficient of the ⌬ ␥ solid curves represent the best fits to the HbO2 data at the rising tumor. The coefficient is the ratio of the HbO2 portion during carbogen inhalation. The fitted equations are concentration change in the vascular bed to that in ͕ Ϫ ͓Ϫ͑ Ϫ ͒͞ ͔͖ ϩ ͕ Ϫ ͓Ϫ͑ Ϫ ͒͞ ͔͖ ͑⌬ vasculature͒͑͞⌬ vein͒ 0.004 1 exp t 21.5 0.3 0.38 1 exp t 21.5 15.6 veins and equals HbO2 HbO2 . and 0.37͕1 Ϫ exp͓Ϫ͑t Ϫ 21.5͒͞14.8͔͖ for the double-exponential and This definition implies that a change in the venous the single-exponential expressions, respectively, with R ϭ 0.97 for ⌬ vein blood oxygenation HbO2 is proportional to a both. change in the Hb oxygenation in the vascular bed, ⌬ vasculature HbO2 . In Eq. ͑12͒, f and ␥ are constants, whereas In general, the Fick principle can be stated as fol- ⌬ vasculature 38 HbO2 is a time-dependent variable. By lows : The rate of change of tracer concentration in ͑ ͒ ⌬ vasculature analogy to Eq. 11 , HbO2 can be solved a regional area of an organ equals the rate at which ⌬ artery the tracer is transported to the organ in the arterial rigorously given a constant input H0 for HbO2 after time 0. Our data ͑Figs. 3 and 8͒ demonstrate circulation minus the rate at which it is carried away ͑ ͒ into the venous drainage, i.e., that changes in the arterial HbO2 SaO2 are much faster than in the vascular bed. Then solving Eq. ͑12͒ leads to dCt ϭ f͑Ca Ϫ Cv͒, (10a) dt vasculature ⌬HbO2 ͑t͒ ϭ ␥H0͓1 Ϫ exp͑Ϫft͞␥͔͒. (13) ͑ ͒ where f is the blood flow or perfusion rate , Ct is the Equation ͑13͒ indicates that, at time t after the onset tracer concentration in tissue, and Ca and Cv are the of respiratory intervention, the change in oxygenated time-varying tracer concentrations in the arterial in- hemoglobin concentration in the tumor vasculature put and the venous drainage, respectively. C can ⌬ vasculature ͑ ͒ a HbO2 t depends on the blood perfusion be measured from a peripheral artery, but C is rel- v rate f, the arterial oxygenation input H0, and the atively difficult to obtain regionally. Therefore a vasculature coefficient of the tumor ␥. ␭ϭ ͞ brain–blood partition coefficient, Ct Cv, was de- As indicated by Eq. ͑8͒, our NIR instrument is able veloped by Kety, and Eq. ͑10a͒ becomes37 to measure an increase in the vascular HbO2 concentration ⌬HbO vasculature. Equation ͑13͒ gives an ex- dC C 2 t ϭ fͩC Ϫ tͪ . (10b) ponential of the same form as that used to fit our dt a ␭ experimental data, indicating that the measured

5238 APPLIED OPTICS ͞ Vol. 39, No. 28 ͞ 1 October 2000 constant implies slow perfusion through a poorly perfused area, whereas a small time constant indicates fast perfusion through a well-perfused area. In the meantime, the ratio of the perfusion rates in these two areas can also be obtained quantitatively. Fur- ␥ ͞␥ Ͼ ͑ ͞ Ͼ ͒ thermore, a ratio of 1 2 1 i.e., A1 A2 1 means that the measured signal results more from region 1 than from region 2 within the measured tumor volume. Therefore, by studying tumor blood oxygenation dynamics and obtaining time constants together with their amplitudes, we can gain important information on regional blood perfusion and vascular structures of the tumor within the measured volume. Our experimental data ͑Table 1͒ reveal that all the measurements can be fitted with the double- ͑ ͒ exponential model equivalently to or better than the Fig. 9. Schematic diagram showing 1 a tumor model with two ␶ ͞␶ ␥ ͞␥ ͑ ͒ single-exponential fitting. Ratios of 1 2, 1 2, vascular perfusion regions, 2 the source and the detector fibers ͞ and their geometry with respect to the tumor model, and ͑3͒ the and f1 f2 are also shown in Table 1 for respective light patterns that propagate in the tumor tissue. A represents a cases. portion of the detected signal, which interrogates the well-perfused region, and B represents another portion of the detected signal, 5. Discussion which passes mainly through the poorly perfused region. We Using NIRS, we have measured relative changes in have assumed that the total detected signal is the sum of A and B. Hbt and HbO2 in breast and prostate rat tumors in response to respiratory intervention. We have observed that respiratory challenge caused the HbO time constant is associated with the blood perfusion 2 ␥ concentration to rise promptly and significantly in rate f and the vasculature coefficient of the tumor in both breast and prostate tumors but that the total the measured area. If the measured volume in- concentration of hemoglobin sometimes increased volves two distinct regions, we then involve with two and sometimes remained unchanged. The dynamic different blood-perfusion rates f1 and f2, two different ␥ ␥ changes of tumor oxygenation can be modeled by ei- vasculature coefficients 1 and 2, or all four. Here ther one exponential term with a slow time constant it is reasonable to assume that the measured signal or two exponential terms with fast and slow time results from both regions, as illustrated in Fig. 9. ͑ ͒ constants. This relation suggests that there may be Consequently, Eq. 13 can be modified with a double- two vascular mechanisms in the tumor that are de- exponential expression and two time constants as tected by the NIRS measurement. As indicated by Eqs. ͑13͒ and ͑14͒, these time constants are inversely ⌬HbO vasculature͑t͒ ϭ ␥ H ͓1 Ϫ exp͑Ϫf t͞␥ ͔͒ 2 1 0 1 1 proportional to the blood-perfusion rates of the mea-

ϩ ␥2 H0͓1 Ϫ exp͑Ϫf2 t͞␥2͔͒ sured volumes of the tumors. Based on the double- ϭ ͓ Ϫ ͑Ϫ ͞␥ ͔͒ exponential model, determination of the two time A1 1 exp f1 t 1 constants and their corresponding amplitudes allows

ϩ A2͓1 Ϫ exp͑Ϫf1 t͞␥2͔͒, (14) us to determine the relations between the two perfusion rates and between the vascular structures, as ␥ where f1 and 1 are the blood-perfusion rate and the expressed in Eq. ͑15͒. Further investigation with vasculature coefficient, respectively, in region 1, f2 more measured quantities may lead to quantification ␥ ϭ␥ ϭ and 2 are the same for region 2, A1 1H0, and A2 of each parameter individually by use of the NIR ␥ ␶ ϭ␥ ͞ 2H0. The two time constants are equal to 1 1 f1 technique. ␶ ϭ␥͞ and 1 2 f2. Then, if A1, A2, and the two time To develop a model for interpreting the NIR data constants are determined from our measurements, taken during carbogen inhalation, we have defined a we arrive at the ratios for the two vasculature coef- vasculature coefficient ␥. It is a proportionality fac- ⌬ vein ⌬ vasculature ficients and the two blood-perfusion rates: tor between HbO2 and HbO2 , i.e., ⌬ vein ϭ⌬ vasculature͞␥ ␥ HbO2 HbO2 . We expect that ␥ A f A ͞A ͑ ͒ ͑ ͒ 1 ϭ 1 1 ϭ 1 2 depends on 1 the oxygen consumption and 2 the , . (15) capillary density of the tumor. If the oxygen con- ␥2 A2 f2 ␶1͞␶2 sumption, the capillary density, or both of the tumor With these two ratios, we can obtain insight into are large, changes in the venous HbO2 concentration the tumor vasculature and blood perfusion. For ex- will be small; if the oxygen consumption, the capillary ␥ ͞␥ ample, a ratio of 1 2 near 1 from a measurement density, or both of the tumor are small, changes in the implies that the vascular structure of the measured venous HbO2 concentration will be large. Further tumor volume is rather uniform. Then the coexist- studies are necessary to learn more about this coef- ence of two time constants reveals two mechanisms of ficient and to confirm our speculation. regional blood perfusion in the tumor. A large time Our current NIR system allows us to quantify the

1 October 2000 ͞ Vol. 39, No. 28 ͞ APPLIED OPTICS 5239 ratio of ␥͞f by using the single-exponential model or measured by use of 19F nuclear magnetic resonance ␥ ͞␥ ͞ 44 to quantify the ratios of 1 2 and f1 f2 by using the spectroscopy to interrogate interstitial oxygenation. double-exponential model. We can obtain impor- In general, well-oxygenated tumor regions had a tant information on the blood perfusion of the tumor: large and rapid response to respiratory challenge, a large time constant usually represents slow blood whereas poorly oxygenated regions were much more perfusion, whereas a small time constant indicates sluggish.45 One would indeed expect changes in fast blood perfusion. The coexistence of two time vascular oxygenation to precede changes in the tis- constants implies a combination of well-perfused and sue, and combined investigations by NIRS and nu- poorly perfused mechanisms of blood perfusion. In- clear magnetic resonance spectroscopy in the future deed, some tumor lines have only 20% to 85% of ves- will provide further insight into the delivery of oxy- sels perfused.41 Furthermore, tumor structures and gen to tumors. oxygen distribution6,42 are highly heterogeneous. Dynamic changes in vascular oxygenation have Therefore it is likely that our measurement detects a been assessed previously by several other techniques. well-perfused region, or a poorly perfused region, or a Following the infusion of Green 2W dye intrave- mixture of both in the tumor, depending on the posi- nously into EMT-6 tumor-bearing mice, Vinogradov tion or the location of the source and the detector of et al.4 were able to image changes in the surface the NIR instrument. vascular pO2. On switching from air to carbogen 22 Hull et al. reported carbogen-induced changes in inhalation, they observed a very rapid increase in pO2 rat mammary tumor oxygenation by using spatially with a rate similar to the fast component, which we resolved NIRS. To compare our results to theirs, we have seen here. Although the phosphorescence applied our curve-fitting procedure to their published method provides vascular pO2, NIR methods gener- hemoglobin saturation curve and obtained a time ally provide HbO2 or SO2 because there is some un- constant of 0.27 min ͑or 16 s͒ for the rising edge, certainty in the local affinity of hemoglobin for tumor which is consistent with our fast component. Their oxygen: the pO2–SO2 dissociation curve is subject to data do not show a slow component, suggesting that pH, temperature, and other allosteric effectors, such their measurement was dominated by active tumor as 2,3-diphosphoglycerate in the immediate milieu. vasculature. This difference may be explained as A promising new approach is the blood-oxygen-level– follows: dependent ͑BOLD͒ contrast 1H MRI, which is sensitive to vascular perturbations. Robinson et al.46 ͑1͒ The tumor volume mentioned in the paper by explored the response to respiratory challenge in var- Hull et al.22 was approximately 1.5 cm3, much ious tumors and showed reversible regional changes smaller than the volumes of the tumors that we mea- on switching from air to carbogen inhalation. In sured ͑in Figs. 3 to 8, the largest tumor was 10.8 cm3, common with our NIR data, their changes were often whereas the smallest tumor was 4.5 cm3͒. biphasic with a large change occurring within the ͑2͒ Their measurement was in reflectance geome- first 2 min and followed by slower increases.46 How- try with multiple detectors located at distances 1 to ever, interpreting the BOLD MRI results is compli- 20 mm away from the source, and in the calculation cated by variations in vascular volume and flow, and the tumor was assumed to be homogenous in order to there is no direct measure of HbO2 in tumors. use diffusion theory. Thus their measurement was The time constants are not source–detector sepa- more sensitive to the superficial area of the tumor, ration sensitive. Equations ͑8͒ and ͑9͒ have demon- ⌬ ⌬ ͞ emphasizing the tumor periphery, which is often bet- strated that HbO2 and Hbt are proportional to 1 d, ter vascularized than the central part of the tu- where d is the source–detector separation. This re- mor.42,43 lation indicates that a different d value will only stretch or compress the entire temporal profile of ⌬ The fast component observed in our tumors is con- HbO2, but it does not change the transient behavior sistent with the rapid changes detected in SaO2 in the of the time response. The same argument can apply leg as measured by use of the pulse oximeter, provid- to the DPF. In this study, we have assumed a DPF ing further evidence that this relates to the well- ratio of 1 for simplicity. If the DPF value is larger ⌬ ⌬ vascularized, highly perfused region of the tumor. than 1, the values of HbO2 and Hbt will decrease The data shown in Fig. 8 in this paper are repre- by a factor of DPF. But this modification does not ␶ ␶ sentative of the measurement of a poorly perfused affect the time constants 1 and 2, which constitute ⌬ region in which the measured tumor was large and the dynamic responses of HbO2 of the tumors to the portion for the fast oxygenation response was respiratory intervention. small. The data given in Figs. 3–5 and 7 resulted Given the evidence for intratumoral heterogeneity from a mixture of well-perfused and poorly perfused from MRI6,46 and histology,47 we believe it will be areas in the tumors and exhibited a mixture of fast important to advance our NIR system to have multi- and slow oxygenation responses to hyperoxygen con- ple sources, multiple detectors, or both to study not ditions. It is reasonable to expect that larger tumors only dynamic but also spatial aspects of blood oxy- have more poorly perfused regions than do smaller genation in tumor vasculature. Nonetheless, we be- tumors. The time constant of the slow component lieve the preliminary results described here are a observed here approaches that observed previously proof of principle for the technique, laying a founda- for changes in tissue pO2 in an AT1 prostate tumor tion for more extensive tests to correlate tumor size

5240 APPLIED OPTICS ͞ Vol. 39, No. 28 ͞ 1 October 2000 with the rates of change of HbO and Hb with respect 2 t ⌬HbO2 ϭ HbO2͑transient͒ϪHbO2͑baseline͒ 22 to respiratory challenge. Although Hull et al. and ␭ ␭ ␭ ␭ ⑀ 2 ⌬␮ 1 Ϫ ⑀ 1 ⌬␮ 2 we have focused on respiratory challenge, we note Hb a Hb a ϭ ␭ ␭ ␭ ␭ , (A4) that previous NIR studies of tumors also examined ⑀ 2 ⑀ 1 Ϫ ⑀ 1 ⑀ 2 Hb HbO2 Hb HbO2 the influence of chemotherapy,21 pentobarbital ⌬ ⌬ overdose,21 ischemic clamping,20 and infusion of where Hb and HbO2 refer to the change in the perfluorocarbon blood substitute.19 These studies deoxyhemoglobin and the oxyhemoglobin concentra- demonstrate the potential versatility of the NIR ap- tions between the baseline condition and the tran- ⌬␮␭ proach and its application for diverse future studies. sient, or perturbed, condition, respectively, and a In summary, we have demonstrated that the NIR represents the change in the absorption coefficient at technology can provide an efficient, real-time, nonin- ␭ relative to the baseline condition. However, our vasive means for monitoring vascular oxygenation current experimental setup with one source and one dynamics in tumors during hyperoxygen respiratory detector does not provide adequate information for quantifying ␮␭ values for a solid rat tumor. Thus we challenge. HbO2 concentrations measured from a both breast and prostate tumors often exhibit a take an approximate approach by using the modified ⌬ ⌬ prompt rise that is followed by a gradual persistence Beer–Lambert relation to calculate Hb and HbO2. throughout the intervention. By developing a he- According to the modified Beer–Lambert law,10 an ͑ ͒ ϭ ͑ ͞ ͒ moperfusion model with two exponential terms and optical density OD can be defined as OD log I0 I ϭ␮ L, where I and I are the incident and the de- fitting the model to the increased HbO2 data, we are a 0 able to recognize two mechanisms for blood perfusion tected optical intensities, respectively, and L is the in the tumor and to quantify the ratios of the two optical path length traveled by light inside the tissue. perfusion rates and those of the two vasculature co- When an organ or a tumor undergoes a change from efficients. Thus the technique can enhance our units baseline condition to a transient condition under derstanding of the dynamics of tumor oxygenation physiological perturbations, a change in the OD at and the mechanisms of tumor physiology under base- wavelength ␭ will occur and can be expressed as

line and perturbed conditions. Moreover, it appears ␭ ␭ ␭ that the NIRS may have a great potential for moni- ⌬OD ϭ OD ͑transient͒ϪOD ͑baseline͒ toring tumor angiogenesis because the method can ϭ log͑I ͞I ͒␭ ϭ ⌬␮␭L␭, (A5) provide information on blood perfusion and oxygen b t a consumption of the measured tumor. where Ib and It are measured optical intensities under baseline and transient conditions, respectively. Appendix A Thus we arrive at

A. Derivation ␭ ␭ ␭ ⌬␮a ϭ log͑Ib͞It͒ ͞L . (A6) It has been shown that, in the NIR range, the major light absorbers in tissue are oxygenated and deoxy- With our current NIR instrument, we can obtain the ͑ ͞ ͒␭1 ͑ ͞ ͒␭2 genated hemoglobin molecules.24,25 With this ratios of Ib It and Ib It from the tumor mea- knowledge, the absorption coefﬁcients ͑in inverse surement. By assuming a constant path length, i.e., ␭1 ␭2 ␭1 ␭2 centimeters͒ at two wavelengths can be associated L ͑baseline͒ϷL ͑baseline͒ϷL ͑transient͒ϷL ͑transient͒ϷL, we next substitute Eq. ͑A6͒ into Eqs. with the concentrations of HbO2 and Hb by ͑A3͒ and ͑A4͒ and arrive at Eqs. ͑5͒ and ͑6͒ for cal-

␭1 ␭1 ␭1 culations of tumor hemoglobin oxygenation dynam- ␮a ϭ ⑀HbHb ϩ⑀HbO HbO2, (A1) 2 ics. Note that Ib, It have been replaced with Ab, At in Eqs. ͑5͒ and ͑6͒. ␮a␭2 ϭ ⑀␭2 Hb ϩ⑀␭2 HbO , (A2) Hb HbO2 2 B. Justiﬁcation The assumption of a constant path length as given where ⑀␭ , and ⑀␭ are the extinction coefﬁcients ͑in Hb HbO2 above makes it possible to use relatively simple equa- inverse centimeters times inverse millimoles͒ of de- tions, for example, Eqs. ͑5͒ and ͑6͒, to quantify the oxygenated and oxygenated hemoglobin, respec- ⌬Hb and the ⌬HbO of tumors under respiratory in- ␭ 2 tively, at wavelength , and HbO2 and Hb are the tervention. However, in principle, the optical path oxyhemoglobin and the deoxyhemoglobin concentra- length L through tissue is wavelength dependent and tions. Because ⑀␭ and ⑀␭ are constants, changes Hb HbO2 could be variable under physiological perturbations. in HbO2 and Hb in tissue vasculature result in Therefore it is useful to know whether the relative ␮␭ changes in a. In turn, changes in HbO2 and Hb can error for calculated ⌬Hb and ⌬HbO caused by this ␮␭ 2 be determined by measuring changes in a at two assumption is within a reasonable range. wavelengths and can be expressed as According to the diffusion approximation, the optical path length L of the NIR light traveling in tissue ⌬Hb ϭ Hb͑transient͒ϪHb͑baseline͒ can be expressed approximately as24 ␭ ␭ ␭ ␭ ⑀ 1 ⌬␮ 2 Ϫ ⑀ 2 ⌬␮ 1 ͱ ␮Ј 1͞2 ϭ HbO2 a HbO2 a 3 s ␭ ␭ ␭ ␭ , (A3) L ϭ d ͩ ͪ , (A7) ⑀ 2 ⑀ 1 Ϫ ⑀ 1 ⑀ 2 ␮ Hb HbO2 Hb HbO2 2 a

1 October 2000 ͞ Vol. 39, No. 28 ͞ APPLIED OPTICS 5241 ␮ where d is the source–detector separation and a and References ␮Ј s are the absorption and the reduced scattering co- 1. L. Gray, A. Conger, M. Ebert, S. Hornsey, and O. Scott, “The efficients, respectively. Because in the NIR region concentration of oxygen dissolved in tissues at time of irradi- ␮Ј ation as a factor in radio-therapy,” Br. J. Radiol. 26, 638–648 the s of tissue is not sensitive to either wavelength or perturbation, we assume that a change in L results ͑1953͒. ␮ 2. M. Ho¨ckel, K. Schlenger, B. Aral, M. Mitze, U. Schaffer, and P. from only a change in a, which is both wavelength and perturbation dependent. With this assumption, Vaupel, “Association between tumor hypoxia and malignant ͑ ͒ progression in advanced cancer of the uterine cervix,” Cancer Eq. A7 leads to Res. 56, 4509–4515 ͑1996͒. 3. T. Y. Reynolds, S. Rockwell, and P. M. Glazer, “Genetic insta- bility induced by the tumor microenvironment,” Cancer Res. ⌬L 1⌬␮a ϭ Ϫ . (A8) ͑ ͒ ␮ 56, 5754–5757 1996 . L 2 a 4. S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, and D. F. Wilson, “Noninvasive imaging of the distribu- Equation ͑A8͒ allows us to determine the relative tion of oxygen in tissues in vivo using near-infrared phos- errors of ⌬L͞L that are caused by ͑a͒ the wavelength phors,” Biophys. J. 70, 1609–1617 ͑1996͒. ␮ ͑ ͒ 5. J. A. O’Hara, F. Goda, K. J. Liu, G. Bacic, P. J. Hoopes, and dependence of a and b the perturbation depen- ␮ ͑ ͒ H. M. Swartz, “The pO2 in a murine tumor after irradiation: dence of a in the tumor. For case a , we calculated this error by using an in vivo electron paramagnetic resonance oximetry study,” Radiat. Res. 144, 222–229 ͑1995͒. 6. R. P. Mason, A. Constantinescu, S. Hunjan, D. Le, E. W. Hahn, 758 782 ␮a Ϫ ␮a P. P. Antich, C. Blum, and P. Peschke, “Regional tumor oxy- 2␮758 genation and measurement of dynamic changes,” Radiat. Res. a 152, 239–245 ͑1999͒. 7. D. T. Delpy and M. Cope, “Quantification in tissue near- under the baseline and the perturbed conditions; for infrared spectroscopy,” Philos. Trans. R. Soc. London B 952, case ͑b͒, we employed 649–659 ͑1997͒. 8. M. Fabiani, G. Gratton, and P. M. Corballis, “Noninvasive ␮␭ ͑transient͒ Ϫ ␮␭ ͑baseline͒ near-infrared optical imaging of human brain function with a a subsecond temporal resolution,” J. Biomed. Opt. 1, 387–398 ␭ ͑ ͒ 2␮a ͑baseline͒ 1996 . 9. R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Ber- at both ␭ϭ758 nm and ␭ϭ782 nm for the error narding, U. Dirnagl, and A. Villringer, “Cerebral blood oxygen- ␮ ation changes induced by visual stimulation in humans,” calculation. The a values used here were taken ͑ ͒ 22 J. Biomed. Opt. 1, 399–404 1996 . from Hull et al. Although the rat tumor used in 10. M. Cope and D. T. Delpy, “A system for long-term measure- their study was different from ours, the absorption ment of cerebral blood and tissue oxygenation in newborn coefficients of the tumors should be in a similar order infants by near-infrared transillumination,” Med. Biol. Eng. and follow a similar dynamic trend. The calculation Comput. 26, 289–294 ͑1988͒. shows that, with 758 and 782 nm under carbogen 11. B. Chance, E. Anday, S. Nioka, S. Zhou, L. Hong, K. Worden, perturbation, the maximum value of ⌬L͞L is 12%. C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, and R. Thomas, “A This result implies that the assumption of a constant novel method for fast imaging of brain function, noninvasively, path length that was used for Eqs. ͑5͒ and ͑6͒ gives with light,” Opt. Express 2, 411–423 ͑1998͒, http:͞͞www.epubs. ͞ rise to a maximal relative error of 12% in L. osa.org opticsexpress. On the basis of Eqs. ͑5͒ and ͑6͓͒or Eqs. ͑7͒ and ͑8͔͒, 12. A. M. Siegel, J. A. Marota, J. Mandeville, B. Rosen, and D. A. ⌬ ͞ ϭϪ⌬ ͞ ⌬ Boas, “Diffuse optical tomography of rat brain function,” in we arrive at X X L L, where X can be HbO2, ⌬ ⌬ Optical Tomography and Spectroscopy of Tissue III, B. Chance, Hb, or Hbt. Thus the assumption of a constant R. R. Alfano, and B. J. Tromberg, eds., Proc. SPIE 3597, 252– path length leads to a maximal relative error of 12% 261 ͑1999͒. for the magnitude of the changes that we detected 13. S. Homma, T. Fukunaga, and A. Kagaya, “Influence of adipose with regard to respiratory challenge. Although 12% tissue thickness on near-infrared spectroscopic signals in the is not completely negligible, the measurement and measurement of human muscle,” J. Biomed. Opt. 1, 418–424 the calculation with the assumption of a constant ͑1996͒. path length are still worthwhile. Such an approach 14. M. Ferrari, Q. Wei, L. Carraresi, R. A. De Blasi, and G. Zac- canti, “Time-resolved spectroscopy of the human forearm,” J. makes it possible, as a first-order approximation, to ͑ ͒ quantify the ⌬Hb and the ⌬HbO of tumors under Photochem. Photobiol. B: Biol. 16, 141–153 1992 . t 2 15. M. Ferrari, R. A. De Blasi, S. Fantini, M. A. Franceschini, B. respiratory intervention, providing deep insight Barbieri, V. Quaresima, and E. Gratton, “Cerebral and muscle into tumor vascular phenomena and mechanisms oxygen saturation measurement by a frequency-domain near- of modulating tumor physiology for therapeutic infrared spectroscopic technique,” in Optical Tomography, enhancement. Photon Migration, and Spectroscopy of Tissue and Model This study was supported in part by The Whitaker Media: Theory, Human Studies, and Instrumentation,B. Chance and R. R. Alfano, eds., Proc. SPIE 2389, 868–874 Foundation RG-97-0083 ͑H. Liu͒, The American Can- ͑ ͒ ͑ ͒ 1995 . cer Society RPG-97-116-010CCE R. P. Mason , and 16. H. Long, G. Lech, S. Nioka, S. Zhou, and B. Chance, “CW The Department of Defense Breast Cancer Initiative imaging of human muscle using near-infrared spectroscopy,” BC962357 ͑Y. Song͒. We thank Peter P. Antich and in Advances in Optical Imaging and Photon Migration,J.G. Eric W. Hahn for their continued collegial support. Fujimoto and M. S. Patterson, eds., Vol. 21 of OSA Trends in

5242 APPLIED OPTICS ͞ Vol. 39, No. 28 ͞ 1 October 2000 Optics and Photonics Series ͑Optical Society of America, 33. J. L. Hintze, NCSS, Version 6.0, User’s Guide II: Statistical Washington, D.C., 1998͒, pp. 256–259. System for Windows ͑Number Cruncher Statistical Systems, 17. B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Kaysville, Utah, 1996͒. Greenfield, and G. Holtom, “Time-resolved spectroscopy of 34. J. B. Fishkin and E. Gratton, “Propagation of photon-density hemoglobin and myoglobin in resting and ischemic muscle,” waves in strongly scattering media containing an absorbing Anal. Biochem. 174, 698–707 ͑1988͒. semi-infinite plane bounded by a straight edge,” J. Opt. Soc. 18. B. M. Fenton, S. F. Paoni, J. Lee, C. J. Koch, and E. M. Lord, Am. A 10, 127–140 ͑1993͒. “Quantification of tumor vasculature and hypoxia by immuno- 35. W. G. Zijlstra, A. Buursma, and W. P. Meeuwsen-van der histochemical staining and HbO2 saturation measurements,” Roest, “Absorption spectra of human fetal and adult oxyhemo- ͑ ͒ Br. J. Cancer 79, 464–471 1999 . globin, deoxyhemoglobin, carboxyhemoglobin, and methemo- 19. H. D. Sostman, S. Rockwell, A. L. Sylva, D. Madwed, G. Cofer, globin,” Clin. Chem. 37, 1633–1638 ͑1991͒. H. C. Charles, R. Negro-Villar, and D. Moore, “Evaluation of 36. H. Liu, C. L. Matson, K. Lau, and R. R. Mapakshi, “Experi- BA 1112 rhabdomyosarcoma oxygenation with microelec- mental validation of a backpropagation algorithm for three- trodes, optical spectrometry, radiosensitivity, and MRS,” dimensional breast tumor localization,” IEEE J. Select. Top. Magn. Reson. Med. 20, 253–267 ͑1991͒. Quantum Electron. 5, 1049–1057 ͑1999͒. 20. F. Steinberg, H. J. Ro¨hrborn, T. Otto, K. M. Scheufler, and C. 37. S. S. Kety, “The theory and applications of the exchange of Streffer, “NIR reflection measurements of hemoglobin and inert gas at the lungs and tissue,” Pharmacol. Rev. 3, 1–41 cytochrome aa in healthy tissue and tumors,” Adv. Exp. 3 ͑1951͒. Med. Biol. 428, 69–77 ͑1997͒. 21. R. G. Steen, K. Kitagishi, and K. Morgan, “In vivo measure- 38. H. Watabe, M. Itoh, V. Cunningham, A. A. Lammertsma, P. ment of tumor blood oxygenation by near-infrared spectros- Bloomfield, M. Mejia, T. Fujiwara, A. K. P. Johes, T. Johes, and copy: immediate effects of pentobarbital overdose or T. Nakamura, “Noninvasive quantification of rCBF using carmustine treatment,” J. Neuro-Oncol. 22, 209–220 ͑1994͒. positron emission tomography,” J. Cerebr. Blood Flow Metab. 22. E. L. Hull, D. L. Conover, and T. H. Foster, “Carbogen-induced 16, 311–319 ͑1996͒. changes in rat mammary tumor oxygenation reported by near- 39. S. S. Kety, “Cerebral circulation and its measurement by inert infrared spectroscopy,” Br. J. Cancer 79, 1709–1716 ͑1999͒. diffusible racers,” Israel J. Med. Sci. 23, 3–7 ͑1987͒. 23. M. S. Patterson, B. Chance, and B. C. Wilson, “Time-resolved 40. A. D. Edwards, C. Richardson, P. Van Der Zee, C. Elwell, J. S. reflectance and transmittance for the noninvasive measure- Wyatt, M. Cope, D. T. Delpy, and E. O. R. Reynolds, “Mea- ment of tissue optical properties,” Appl. Opt. 28, 2331–2336 surement of hemoglobin flow and blood flow by near-infrared ͑1989͒. spectroscopy,” J. Appl. Physiol. 75, 1884–1889 ͑1993͒. 24. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, 41. H. J. J. A. Bernsen, P. F. J. W. Rijken, T. Oostendorp, and A. J. “Quantitation of time- and frequency-resolved optical spectra van der Kogel, “Vascularity and perfusion of human gliomas for the determination of tissue oxygenation,” Anal. Biochem. xenografted in the athymic nude mouse,” Br. J. Cancer 71, 195, 330–351 ͑1991͒. 721–726 ͑1995͒. 25. H. Liu, A. H. Hielscher, F. K. Tittel, S. L. Jacques, and B. 42. R. P. Mason, P. P. Antich, E. E. Babcock, A. Constantinescu, P. Chance, “Influence of blood vessels on the measurement of Peschke, and E. W. Hahn, “Noninvasive determination of tu- hemoglobin oxygenation as determined by time-resolved mor oxygen tension and local variation with growth,” Int. J. ͑ ͒ reflectance spectroscopy,” Med. Phys. 22, 1209–1217 1995 . Radiat. Oncol. Biol. Phys. 29, 95–103 ͑1994͒. 26. S. J. Matcher, M. Cope, and D. T. Delpy, “In vivo measure- 43. B. P. J. van der Sanden, A. Heerschap, A. W. Simonetti, ments of the wavelength dependence of tissue-scattering coef- P. J. F. W. Rijken, H. P. W. Peters, G. Stuben, and A. J. van der ficients between 760 and 900 nm measured with time-resolved Kogel, “Characterization and validation on noninvasive oxy- ͑ ͒ spectroscopy,” Appl. Opt. 36, 386–396 1997 . gen tension measurements in human glioma xenografts by 27. E. W. Hahn, P. Peschke, R. P. Mason, E. E. Babcock, and P. P. 19F-MR relaxometry,” Int. J. Radiat. Oncol. Biol. Phys. 44, Antich, “Isolated tumor growth in a surgically formed skin 649–658 ͑1999͒. pedicle in the rat: a new tumor model for NMR studies,” 44. S. Hunjan, R. P. Mason, A. Constantinescu, P. Pescheke, E. W. Magn. Reson. Imaging. 11, 1007–1017 ͑1993͒. Hahn, and P. P. Antich, “Regional tumor oximetry: 19F NMR 28. Y. Yang, H. Liu, X. Li, and B. Chance, “Low-cost frequency- spectroscopy of hexafluorobenzene,” Int. J. Radiat. Oncol. Biol. domain photon migration instrument for tissue spectroscopy, Phys. 41, 161–171 ͑1998͒. oximetry, and imaging,” Opt. Eng. 36, 1562–1569 ͑1997͒. 29. H. Y. Ma, Q. Xu, J. R. Ballesteros, V. Ntziachristors, Q. Zhang, 45. S. Hunjan, D. Zhao, A. Constantinescu, E. W. Hahn, P. P. and B. Chance, “Quantitative study of hypoxia stress in piglet Antich, and R. P. Mason, “Tumor oximetry: an enhanced brain by IQ phase modulation oximetry,” in Optical Tomogra- dynamic mapping procedure using fluorine-19 echo planar phy and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, magnetic resonance imaging,” Int. J. Radiat. Oncol. Biol. Phys. ͑ ͒ and B. J. Tromberg, eds., Proc. SPIE 3597, 642–649 ͑1999͒. to be published . 30. P. R. Bevington, Data Reduction and Error Analysis for the 46. S. P. Robinson, F. A. Howe, L. M. Rodrigues, M. Stubbs, and Physical Sciences ͑McGraw-Hill, New York, 1969͒. J. R. Griffiths, “Magnetic resonance imaging techniques for 31. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vet- monitoring changes in tumor oxygenation and blood flow,” terling, Numerical Recipes ͑Cambridge U. Press, Cambridge, Semin. Radiat. Oncol. 8, 198–207 ͑1998͒. 1988͒. 47. B. M. Fenton, “Effects of carbogen plus fractionated irradiation 32. KaleidaGraph, Version 3.08 ͑Synergy Software, 2457 Perki- on KHT tumor oxygenation,” Radiother. Oncol. 44, 183–190 omen Avenue, Reading, Pa. 19606, 1996͒. ͑1997͒.

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