INTRODUCTION

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THE PRESENCE OF HYPOXIA in tumors has long been known to adversely affect the sensitivity of tumors to radiation therapy (44). More recently hypoxia has been shown to exert a selective pressure for the survival of those cells with lower apoptotic potential (15), to alter gene expression such as those involved in cell cycle regulation and cytokine production (10), to increase mutation frequency (35), and to impact treatment outcome and patient survival (3, 19, 20, 32, 33). Significant portions of both human and animal tumors have been shown to be hypoxic by direct measurement with oxygen electrodes (2, 46), optical oxygen sensors (9), and optical fluorescent techniques (17) or by use of hypoxia markers (24).

Despite the importance and prevalence of tumor hypoxia, its exact origins have still not been totally elucidated. Typically hypoxia is divided into two categories: "chronic" and "perfusion limited" (or acute). Chronically hypoxic cells are cells in a low-oxygen environment created largely by their distance from the blood vessels and the metabolic activity of the intervening cells (44). The second category of hypoxic cells, the acutely or transiently hypoxic cells, experience low PO₂ as a result of transient changes in the oxygen supply (4). Classically this "perfusion-limited" hypoxia has been attributed to transient blockages in the vessels or collapse of tumor vessels, leading to temporary cessation of blood flow (BF) or intermittent flow (33).

The term intermittent flow typically implies that BF in the vessel temporarily shuts down completely, causing transient tissue hypoxia. When the vessel reopens, cells dependent on that vessel for oxygen are reoxygenated. Whereas intermittent flow definitely occurs in tumors (31) and probably results in intermittent tumor hypoxia, another subtler possibility for intermittent hypoxia may be fluctuations in red blood cell (RBC) flux through a vessel. Large fluctuations in RBC flux and perivascular PO₂ occur in R3230Ac mammary carcinoma implanted in the dorsal window chamber of rats (12, 26). Similar heterogeneity in RBC flux has also been demonstrated in other solid tumor models (6, 18) and in human tumors in patients (18) as measured by laser-Doppler flowmetry (LDF). It has been theoretically demonstrated that such fluctuations in RBC flux can have significant effects on tumor interstitial PO₂ and the hypoxic fraction of tumors (26).

Although changes in RBC flux and perivascular PO₂ have been demonstrated in vivo, the time course of changes in parenchymal PO₂ in a solid tumor has never been measured. The hypothesis of the current study was that interstitial PO₂ would fluctuate and that this fluctuation would differ from that seen in a normal tissue such as muscle. To address this hypothesis, R3230Ac mammary adenocarcinomas were implanted into the hindlimbs of Fischer 344 rats. We measured PO₂ at a single site in 1-cm-diameter tumors for 36-125 min using recessed-tip oxygen microelectrodes. Tumor BF was measured simultaneously using LDF, and arterial blood pressure (BP) was monitored as well. Similar experiments were performed in the hindlimb muscle of rats. To quantitatively characterize the fluctuations, the Fourier power spectra of the PO₂ and LDF recordings in tumor and muscle were determined. A portion of these data was qualitatively presented in an earlier study (11), but Fourier analysis, which is the emphasis of this study, was not included.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Animals

Muscle PO₂ and BF were measured in seven non-tumor-bearing Fischer 344 rats. We exposed the left quadriceps muscle by removing a patch of skin on the left thigh to permit insertion of the oxygen microelectrode later.

Oxygen Microelectrodes

The microelectrodes were polarized at 0.7 V using a commercial polarizing box and picoammeter unit (Chemical Microsensor no. 1201, Diamond General, Ann Arbor, MI). Electrodes were calibrated before and after experiments in a saline-filled tonometer alternately bubbled with 0%, 5%, 15%, or 21% oxygen (balance nitrogen). The saline was warmed to 37°C. An in vivo dead value was also obtained by recording the microelectrode current in the tissue after euthanasia of the rat with an overdose of pentobarbital sodium. The average sensitivity of the microelectrodes used in this study was 1.27 ± 0.72 mmHg/pA (means ± SD; 16 electrodes).

Experimental Setup

A micromanipulator (model MO102E, Narishige, Narishige, Japan) was positioned so that a dummy electrode could reach the exposed tumor or muscle surface, which was covered by a drop of saline. The actual microelectrode was then placed in the micromanipulator and advanced into this saline droplet. We allowed the electrode to polarize for several minutes in the saline before we advanced it into the tumor or muscle. The microelectrode was moved several millimeters into the tissue until a clearly nonzero PO₂ current was obtained, so that the PO₂ had an opportunity to either increase or decrease. This was particularly necessary in the tumor, which had many very hypoxic (even anoxic) areas. Because the goal of this study was to look at fluctuations in PO₂ and examine them as indicators of transient hypoxia, we did not want to leave an electrode in an area that may have been chronically hypoxic with PO₂ readings near zero. The signal from the microelectrode was sent to the same data acquisition board and software as the BP (AT-CODAS) and digitized at 25 Hz.

BP, PO₂, and BF were recorded continuously for up to 125 min. If the mean arterial BP (MABP) dropped below 80 mmHg, the experiment was terminated early. At the end of the recording time, an overdose of pentobarbital sodium was injected intravenously. The recordings of all parameters continued for at least 5 min after death. The PO₂ value after death was used in the final electrode calibration as a true in vivo zero as described previously (14). The BF values from the LDF signal recorded after death were used as the zero value, and the values were subtracted from the recorded values to produce a corrected BF. Any probes that did not show a decrease in BF after death were excluded from the analysis.

Fourier Analysis

The frequency characteristics of the instrumentation had no impact on the Fourier analysis. The oxygen microelectrodes respond within 40-100 ms (39), which is much faster than the fluctuations of interest in this study. Although the high-frequency response of the Chemical Microsensor no. 1201 is somewhat limited in the range (200 pA full scale) that was used in most cases, its cutoff (3 dB) frequency was measured to be 2.3 Hz (138 cycles/min), and the attenuation was 50% at 4.1 Hz (246 cycles/min). According to the manufacturer, the Oxford laser-Doppler array has a cutoff frequency of 5 Hz (300 cycles/min). Because these cutoff frequencies are relatively high, and the resulting attenuations had little or no effect on the apparent power within the frequency range of interest, the instrumentation should not have contributed to or biased the PO₂ and LDF signals.

Two different record lengths were analyzed using the Fourier analysis: 5.5- to 6.8-min and 32.8- to 34.1-min records. Consecutive data points (8,192) recorded at either 25 or 20 Hz constituted the short-term records (5.5 min for PO₂ and BP; 6.8 min for BF). Each record overlapped the neighboring records by 50%. For example, the second short-term Fourier analysis of a PO₂ recording covered data from 2.73 to 8.19 min, whereas the third covered 5.46 to 10.92 min. The long-term (33 min for PO₂ and BP; 34 min for BF) analysis was performed on records that contained 49,146 points (BP and PO₂) or 40,960 points (BF). The records were averaged, over every 5 or 6 points by the software, to obtain files 8,192 points in length. Again each record overlapped the neighboring records by 50%. For example, the second long-term Fourier analysis of a PO₂ recording covered data from 16.38 to 49.15 min, whereas the third analysis covered 32.76 to 65.53 min.

Each type of analysis yielded different information. Obviously many 5.5-6.8 min spectra could be generated for each recording, so the time dependence of the fluctuations could be easily shown using this type of analysis. Unfortunately, this information was gained at the cost of frequency resolution, because fewer points were included in the analysis. Resolution of the low-frequency range was obtained by analyzing 33- to 34-min segments of the recordings.

Data Analysis

Frequency. An informative way to view and compare frequency information from Fourier power spectra is to examine the frequencies at which the power peaks. This technique was recently used by Buerk and Riva (5) to compare power spectra of nitric oxide and BF in the optic nerve head. In this study, the analysis was used as follows: the frequencies at which the first 20 power peaks occurred were determined for each power spectrum. We then pooled peak frequencies for each tissue type, and we plotted the peak frequencies against each other. Differences in the dominant frequencies between tissues appeared as a deviation of the points from the identity line.

Power and magnitude of fluctuations. The power of the Fourier power spectra (i.e., the magnitude of the fluctuations) was analyzed in two different ways. The simplest method of comparing power between spectra is to look at the total power over a given frequency range (1). Because most of the power in the present study was at very low frequencies, the range chosen for analysis was 0-10 cycles/min. The total power of a spectrum was obtained by summation of all powers between 0 cycles/min and a given frequency. The total cumulative power was plotted as a function of frequency, and comparisons were made. The total power between 0 and 10 cycles/min was also calculated, and this parameter was designated the total low-frequency power (TLFP).

Statistics

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Tumor PO₂ Fluctuations

Tumor PO₂ recordings. Tumor PO₂ was measured at 13 different sites in 9 tumors. The duration of the measurement period ranged from 36 to 125 min with means ± SD of 84 ± 22 min. The tumors were generally very hypoxic, and the electrode needed to be moved along the insertion track to find a location where a nonzero PO₂ could be recorded. The average PO₂ during the first 10 min of recording was 15.2 ± 10.5 mmHg (means ± SD; n = 13) with a range of 1.3 to 38.5 mmHg and a median of 12.9 mmHg. Overall there was a tendency for PO₂ to decrease during the measurement period. At the end of the recording time, the average PO₂ over 10 min was 6.9 ± 9.3 mmHg (means ± SD; n = 13) with a range of 0 to 33.7 mmHg and a median of 3.7 mmHg. The difference between the starting and ending PO₂ was significant (P < 0.01; Wilcoxon test). This point will be addressed in the DISCUSSION.

View larger version (35K): [in this window] [in a new window]   Fig. 1.   Fluctuation of PO2 in a subcutaneously implanted R3230Ac tumor in rat hindlimb (rat 1). A: continuous recording of PO2 over a 77-min period. Graphed data are 10-s averages of original recording. B: short-term Fourier analysis of overlapping 5.5-min segments of record. See METHODS for details. C: long-term Fourier analysis of 3 overlapping 33-min segments of record. See METHODS for details.

View larger version (31K): [in this window] [in a new window]   Fig. 2.   Fluctuation of PO2 in a subcutaneously implanted R3230Ac tumor in the rat hindlimb (rat 5b). A: continuous recording of PO2 over 97-min period. Graphed data are 10-s averages of original recording. B: short-term Fourier analysis of overlapping 5.5-min segments of record. See METHODS for details. C: long-term Fourier analysis of 4 overlapping 33-min segments of record. See METHODS for details. Scale of power axis is truncated to better visualize low-amplitude power. Initial peaks (0.03 cycles/min) for 2nd and 4th measurement periods (32.8 and 65.6 min) are 2.78 and 4.67 mmHg2, respectively.

Fourier analysis of tumor PO₂ fluctuations. Fourier analysis of the tumor PO₂ recordings showed that the fluctuations typically occurred at very low frequencies (<1 cycle/min) and were relatively large in magnitude. As noted in METHODS, two different analyses were carried out: a short-term (5.5 min) and a long-term (33 min) analysis. In Fig. 1, B and C, and Fig. 2, B and C, both types of analysis are shown. In Fig. 1B and Fig. 2B the results of the short-term Fourier analysis are shown, whereas Fig. 1C and Fig. 2C show the long-term analysis.

Tumor BF Fluctuations

Tumor BF recordings. In addition to PO₂, tumor BF was simultaneously measured in the same nine rats at 21 different sites. In general, all of the probes showed some fluctuation in tumor BF. Figure 3 shows one of the two traces of tumor BF recorded in rat 1 over the same 77 min as the PO₂ in Fig. 1A. This particular LDF probe showed many large, slow changes in tumor BF of ~10-30% (Fig. 3A). At some time points, tumor BF dropped ~40% compared with the average baseline and then rebounded. The other probe in this tumor also showed large fluctuations in tumor BF (not shown). Whereas some of the characteristics were similar, the temporal characteristics of the two recordings made at different sites in the same tumor were very different. Tumor BF also fluctuated in rat 5b, but at a smaller amplitude (not shown). Both recordings in that particular tumor were dominated by a slow 20-40% increase at 55 min.

View larger version (35K): [in this window] [in a new window]   Fig. 3.   Fluctuation of laser-Doppler flowmetry (LDF) tumor blood flow (BF) in a subcutaneously implanted R3230Ac tumor rat hindlimb (rat 1). A: continuous recording of tumor BF over a 77-min period. The graphed data are 10-s averages of original recording. B: short-term Fourier analysis of overlapping 6.8-min segments of record. See METHODS for details. C: long-term Fourier analysis of 3 overlapping 34-min segments of record. See METHODS for details.

Fourier Analysis of Tumor Blood Flow Fluctuations

The characteristics of the short-term power spectra are best summarized by examining the average TLFP values. The average short-term TLFP value for the first tumor BF recording in rat 1 (Fig. 3) was 253.7 ± 181.0%² (means ± SD, n = 21) with a range of 23.3-654.8%² and a median of 189.9%². The average short-term TLFP value for the second tumor BF recording in rat 1 (not shown) was 248.9 ± 88.3%² (means ± SD, n = 21) with a range of 162.8-474.5%² and a median of 219.0%². These values, particularly the standard deviation, show how different these traces were. The TLFP values for all of the short-term tumor BF spectra analyzed in tumors are summarized in Table 2.

As was the case for the PO₂ recordings, more detailed information on the nature of the tumor BF fluctuations can be gained by looking at the long-term power spectra. Figure 3C shows the power spectra for three consecutive, overlapping 34-min recording periods from the tumor BF recording in Fig. 3A. In this example, there was significant activity at frequencies out to and beyond 2 cycles/min. The dominant frequency remained relatively stable at 0.23 or 0.17 cycles/min, although the maximum power at those frequencies increased in the third 34-min period (Fig. 3C). In contrast, in the tumor BF recording of the second LDF probe, the dominant frequency changed from 0.56 to 0.03 to 0.64 cycles/min during the three recording periods, and the maximum power at those three frequencies was 44, 43, and 21%², respectively (not shown). Thus the nature of the fluctuations measured by these two probes was very different.

Again, the results of the long-term spectral analysis can be summarized by looking at the TLFP values. The TLFP values from the three spectra from the first recording in rat 1 (Fig. 3) were 128, 179, and 337%². For the tumor BF signal measured by the second LDF probe, the TLFP values were 311, 307, and 219%². The long-term TLFP values for all 21 measured tumor sites are summarized in Table 2.

Although most power spectra of the tumor BF recordings were dominated by the low-frequency fluctuations, there were also higher frequency components corresponding to respiration rate and heart rate, typically ~50-60 and 300-400 cycles/min, respectively. These data are not shown here, because these higher frequency signals were not seen in the PO₂ recordings and had no effect on fluctuations in oxygenation. Thus the fluctuations of interest in the current study are primarily those below 2 cycles/min.

Muscle PO₂ Fluctuations

Muscle PO₂ recordings. Muscle PO₂ was measured at seven sites in seven rats. The duration of the measurement period ranged from 77 to 92 min with a mean ± SD of 89 ± 5 min. In contrast with the tumors, the muscles were generally well oxygenated, and the electrode typically needed to be simply inserted into the muscle to find a location at which a nonzero PO₂ could be recorded. The average PO₂ during the first 10 min of recording was 14.0 ± 8.4 mmHg (means ± SD; n = 7) with a range of 5.1-23.5 mmHg and a median of 13.3 mmHg. Qualitatively muscle PO₂ showed some fluctuations, but the fluctuations seemed to be much smaller in magnitude than those seen in the tumor. The PO₂ tended to decrease over the course of the recording period, but it never dropped to 0 mmHg, as occurred in some tumors. At the end of the recording period, the average PO₂ over the last 10 min was 10.9 ± 5.7 mmHg (means ± SD; n = 7) with a range of 4.0-17.4 mmHg and a median of 13.2 mmHg. The difference between the starting and ending PO₂ was not significant (P > 0.05, Wilcoxon test).

View larger version (31K): [in this window] [in a new window]   Fig. 4.   Fluctuation of PO2 in the quadriceps muscle in rat hindlimb (rat 19). A: continuous recording of PO2 over a 90-min period. Graphed data are 10-s averages of original recording. B: short-term Fourier analysis of overlapping 5.5-min segments of record. See METHODS for details. C: long-term Fourier analysis of 4 overlapping 33-min segments of record. See METHODS for details. Scale of the power axis is truncated to better visualize low-amplitude power. Initial peak (0.03 cycles/min) for 1st measurement period (16.4 min) is 4.85 mmHg2.

Fourier analysis of muscle PO₂ fluctuations. The behavior described above is verified when the Fourier analyses for this experiment are examined. The short-term (5.5 min) analysis shows that there was only significant fluctuation in PO₂ in the first few minutes of the recording and between 30 and 50 min (Fig. 4B). The average short-term TLFP value for this recording was 0.60 ± 0.59 mmHg² (means ± SD, n = 32) with a range of 0.22-2.84 mmHg² and a median of 0.32 mmHg². The 6-min TLFP values for all of the muscle PO₂ recordings are summarized in Table 1.

Muscle Blood Flow Fluctuations

Muscle BF recordings. In addition to PO₂, muscle BF was simultaneously measured in the same 7 rats at 13 different sites. Similar to the tumor LDF measurements, all of the probes showed some fluctuation in muscle BF. The muscle BF traces from two LDF probes in the same muscle as described in the previous section are shown in Fig. 5A. The two traces of muscle BF were recorded over the same 90 min as the PO₂ in Fig. 4A. Both probes showed relatively high-frequency changes in muscle BF with magnitudes of ~5-10%. Whereas one probe remained relatively stable around the mean BF value (LDF 2), the other LDF probe fluctuated at a much lower frequency (LDF 1).

View larger version (36K): [in this window] [in a new window]   Fig. 5.   Fluctuation of LDF muscle BF in the quadriceps muscle in the rat hindlimb (rat 19). A: continuous recordings of muscle BF by 2 different LDF probes over a 92-min period. Graphed data are 10-s averages of original recording. B: short-term Fourier analysis of overlapping 6.8-min segments of record from probe 1 (LDF 1). See METHODS for details. C: long-term Fourier analysis of 3 overlapping 34-min segments of the record from probe 1 (LDF 1). See METHODS for details. Scale of the power axis is truncated to better visualize low-amplitude power and to simplify comparison with Fig. 3. First peak (0.03 cycles/min) for first measurement period (17.0 min) is 138.0%2.

Comparison of Tumor and Muscle

Tumor and muscle PO₂ fluctuations. FREQUENCY DISTRIBUTION. A comparison of the PO₂ power spectra from muscle and tumor revealed no difference between the peak frequencies (Fig. 6A). None of the first 20 peak frequencies was statistically different between the two tissues (Mann-Whitney U-test, P > 0.12).

View larger version (19K): [in this window] [in a new window]   Fig. 6.   A: median peak frequencies from power spectra of PO2 recordings from tumor and muscle. Solid line is identity line; error bars show 25th and 75th percentiles of data. B: median peak power at each dominant peak frequency from the power spectra of the PO2 recordings from tumor and muscle. Solid line is identity line; error bars show 25th and 75th percentiles of data. Inset: blowup of curves over 0-0.10 mmHg2. * Significantly different (P < 0.001; Mann-Whitney U-test). All points shown in inset are significantly different (P < 0.001; Mann-Whitney U-test).

View larger version (22K): [in this window] [in a new window]   Fig. 7.   Median cumulative power of the power spectra for tumor and muscle PO2 recordings. Inset: blowup of curves over 0-2 cycles/min.

Tumor and muscle BF fluctuations. FREQUENCY DISTRIBUTION. A direct comparison of the peak frequencies in muscle BF and tumor BF showed that there was more low-frequency BF activity in the tumor (Fig. 8A). For example, the median sixth peak frequency in tumor was only 0.468 cycles/min, compared with 0.558 cycles/min in muscle (P < 0.001; Mann-Whitney U-test).

View larger version (17K): [in this window] [in a new window]   Fig. 8.   A: median peak frequencies from the power spectra of the LDF BF recordings from tumor and muscle. Solid line is identity line; error bars show the 25th and 75th percentiles of the data. * Significantly different (P < 0.02; Mann-Whitney U-test). B: median peak power at each dominant peak frequency from power spectra of the LDF BF recordings from tumor and muscle. Solid line is identity line; error bars show 25th and 75th percentiles of data. Inset: blowup of the curves over the very low power range (0-3 or 0-6%2). All points shown in inset are significantly different (* P < 0.001; Mann-Whitney U-test).

View larger version (24K): [in this window] [in a new window]   Fig. 9.   Median cumulative power of the power spectra for tumor and muscle LDF BF recordings. Inset: blowup of the curves over 0-2 cycles/min.

Possible Correlation Between Blood Flow and PO₂

Tumor BF and PO₂ fluctuations: frequency and magnitude. The relationship between tumor PO₂ and tumor BF is summarized for all of the data in Fig. 10A. The peak frequency comparison showed a clear upward shift above the identity line. Beyond the fourth power peak, the frequencies of the PO₂ power peaks were higher than those of the corresponding peaks in the tumor BF power spectra (P < 0.006, n = 79 spectra). In other words, there tended to be more power peaks in the tumor BF signal compared with the PO₂ signal, indicating slightly more low-frequency activity in the tumor BF than in the PO₂ signal.

View larger version (20K): [in this window] [in a new window]   Fig. 10.   Median peak frequencies from the power spectra of the PO2 and LDF BF recordings from tumor (A) and muscle (B). Solid line is identity line, and error bars show 25th and 75th percentiles of data. * Significantly different (P < 0.006; Wilcoxon test).

Muscle BF and PO₂ fluctuations: frequency and magnitude. The relationship between BF and PO₂ in the muscle was different from that seen in the tumor (Fig. 10B). In the muscle, the peak frequencies of the PO₂ power spectra and the muscle BF spectra were almost identical, indicating that there was some activity at almost all of the same frequencies in both signals (P > 0.25, n = 50 spectra). When the power spectra peak frequencies from the individual experiments were compared, the slopes of the correlations were spread out almost equally below and above 1 with 46% of the slopes under 1 (Table 3).

Possible Role of BP Fluctuations

The power spectra of the blood pressure recordings were dominated by the higher frequency components corresponding to respiration rate and heart rate, typically ~50-60 and 300-400 cycles/min, respectively. Usually there was also some low-frequency power, in the range of 1-10 cycles/min. This power was evident in many tumor and muscle experiments, in which BP could fluctuate by 5-10 mmHg during the recording time (data not shown).

Tumor and muscle PO₂ and BP fluctuations: frequency and magnitude. The major reason for examining the BP traces using Fourier analysis was to determine if changes in BP were related to changes in tissue PO₂ or BF. To test whether there was any relationship between tissue PO₂ and BP, the frequencies of the power peaks in the two power spectra were compared, as was done for PO₂ and BF. An examination of power spectra from the individual experiments revealed that there were substantial differences between the power spectra in tumors (Table 3). The median slope was 0.998 with exactly equal spread in the values above and below 1. The 25th and 75th percentile values were also very far from 1, indicating large spread in the data. Thus there was no clear relationship between tumor PO₂ and BP.

Tumor and muscle BF and BP fluctuations: frequency and magnitude. The relationship between tissue BF fluctuations and BP fluctuations was also examined by comparing the frequencies of the power peaks. There was more low-frequency activity in the tumor BF spectrum than in the BP spectrum, as evidenced by a significant shift of the correlation lines to the right of the identity line. The median slope of the 79 correlation lines was 0.889, and 77.2% of the correlations had slopes under 1.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

In this study temporal changes in tumor and muscle oxygenation have been characterized for the first time using Fourier spectral analysis. PO₂ in both tissues fluctuated at very low frequencies (<1-2 cycles/min), but the magnitudes of fluctuations in tumor were larger than those seen in muscle. Laser-Doppler BF signals were simultaneously measured in the tissues and were also subjected to Fourier analysis. Both tissues showed low-frequency fluctuations in BF, but there was more low-frequency activity in the tumor and the magnitude of the BF fluctuations tended to be higher in tumor than in muscle. In tumor, there was more low-frequency activity in BF compared with PO₂, whereas in muscle there was no significant difference between the peak frequencies of BF and PO₂. None of the fluctuations could be directly correlated with changes in BP.

Decrease in Mean Tumor PO₂ During Measurement Period

The behavior of the tumor PO₂ can be roughly subdivided into three different types. In four cases the tumor PO₂ gradually dropped to zero after 22-68 min of recording and remained at zero for the duration (~20 to 40 min). In three other cases, the PO₂ fluctuated up and down during most of the experiment but eventually ended up at a mean PO₂ much lower than the starting value. In one example, the PO₂ started at 29 mmHg, rose to 40 mmHg after 55 min, and decreased to 12 mmHg by 90 min. In the other six cases, the PO₂ was fluctuating around a new value within 6 mmHg of the starting value. In two of these six experiments the end value was higher. An example in which the ending PO₂ was lower is shown in Fig. 1A. Whereas the four cases in which PO₂ dropped to zero may have possibly been caused by some local tissue damage, we could not prove this and saw no reason to exclude these data. As already noted, we selected a starting PO₂ that was clearly distinguishable from zero to permit the PO₂ to transiently fluctuate up or down. A point already at zero could easily have been located in a chronically hypoxic area, where the PO₂ would have remained at zero throughout the experiment, regardless of local changes in flow. By choosing a point with a relatively high PO₂, we were also selecting for points which would more likely decrease than increase. This is particularly true for the cases that dropped more than 6 mmHg, including those which dropped to zero. If the PO₂ was high initially because it was near a blood vessel, a decrease in local perfusion would have dropped the PO₂ significantly, even to zero. The converse of that scenario is much less likely, because we would never have selected a point near a closed or low-perfused vessel that might have increased its flow later. Therefore, the selection was biased toward values that might decrease by large amounts but would most likely not increase by similar magnitudes.

Tumor and Muscle PO₂ Fluctuations

The PO₂ fluctuations in tumor and muscle reported here occurred over a much lower frequency range than those reported in neural tissue, but the range is very similar to that noted for gracilis muscle. This is not too surprising, because neural tissue would be expected to have very fine control over BF and oxygenation. Because muscle can and often does carry out glycolysis, it is not essential for that tissue to maintain finely controlled oxygen levels. Tumor, of course, would be expected to exert little or no control over its oxygen supply. Alternatively, brain and retina might require more exquisite, relatively high-frequency control of oxygen levels. This difference in the needs and natures of the tissues may explain the difference in the characteristics of the PO₂ fluctuations found in the tissues.

The fluctuations in PO₂ must be caused by either changes in oxygen delivery or oxygen consumption or by a combination of the two. Although changes in oxygen consumption cannot be ruled out, it is difficult to derive a hypothesis to explain PO₂ fluctuations based solely on changes in oxygen consumption. Although not totally dismissing the possibility of changes in consumption, most previous studies have attributed the changes in local PO₂ primarily to alterations in oxygen supply, i.e., BF (1, 4, 47). If the fluctuations are indeed primarily attributable to changes in local BF, it is necessary to postulate circulatory or hemodynamic mechanisms that could be responsible for the changes in PO₂ at the observed frequencies. Possible mechanisms behind the PO₂ and BF fluctuations will be discussed in a later section.

Tumor and Muscle BF Fluctuations

In this study almost all of the spontaneous fluctuations in BF occurred at very low frequencies below 2 cycles/min. Usually very little activity of significant magnitude was seen between 2 and 30 cycles/min. In most power spectra there was evidence of activity at higher frequencies corresponding to respiration rate and heart rate, typically ~50-60 and 300-400 cycles/min, respectively. This was true not only of the tumor tissue, but of the muscle tissue as well. Thus when these data are compared with previous LDF data, several differences must be kept in mind. First, unlike the results from other studies in other tissues, there was little activity between 2 and 30 cycles/min. This means that there was an absence of activity in the BF signal at those frequencies typically associated with vasoactivity. Second, the significant low-frequency activity was below 1-2 cycles/min, where most other investigators found little or no activity. The reasons behind these discrepancies could be real or artifact.

There are several possible reasons for a lack of significant LDF activity at frequencies associated with vasomotor activity. One possibility may have been the use of pentobarbital as the anesthetic. It has been shown that intravenous doses of 35 mg/kg can cause loss of vasomotor activity in hamster vessels (7). Whereas it may be possible that pentobarbital diminished vasoactivity in the present study, it is unlikely that it would have totally blocked any spontaneous activity, because we have previously demonstrated diameter fluctuations in the window chamber preparation in the same Fischer 344 rats under the same pentobarbital anesthesia under control conditions (12) and during hypotensive episodes (41). Another possibility is that these spectra represent the actual BF fluctuations in tumor and muscle and that these tissues simply do not exhibit higher frequency vasoactivity (2-20 cycles/min). Certainly this could well be true in tumor, where there is no direct evidence of high-frequency fluctuations in BF, but there is evidence of very low-frequency (<0.5 cycles/min) fluctuations in both murine and human tumor LDF (6, 18). In addition very slow fluctuations in erythrocyte flux have been demonstrated in microvessels of a transplanted tumor in the rat (26). Interestingly, the humans in whom slow LDF fluctuations were found were not anesthetized, which again suggests that anesthesia has little effect on this type of fluctuant behavior. One might expect muscle to show more classical vasoactivity over the entire frequency range; however, there are several examples of LDF recordings in nontumor tissues, including muscle, which showed little activity at frequencies between 10 and 30 cycles/min. For example, Buerk and Riva (5) showed that most of the activity in the power spectra of LDF recordings in the cat optic nerve head was below 10 cycles/min. The vast majority of the fluctuations were between 0 and 5 cycles/min. In skeletal muscle, LDF recordings under control conditions did not show fluctuations at frequencies associated with vasomotion (27).

There is little or no mention in the literature of slower fluctuations at frequencies under 1 cycle/min, although some studies show significant power peaks at 1 or 2 cycles/min (5, 21). This is most likely a result of the short durations of the measurement periods analyzed in previous studies. Typically, BF is measured for 5 min or less (e.g., Refs. 5 and 21). Because the frequency resolution of the spectrum is a function of the number of sampled points, the shorter the measurement period is, the lower the resolution will be. For example, in this study, 5.5-min records were analyzed using Fourier analysis (Figs. 1B, 2B, and 5B). The resolution of the power spectra from these recordings was 0.00305 Hz or 0.1831 cycles/min. This translates into five points between 0 and 1 cycles/min. To improve the very low-frequency resolution, we chose to analyze recordings of over 33 min, which yielded spectra with a resolution of 0.03 cycles/min. Such long recordings of laser-Doppler BF have not been analyzed before. Thus in this study high-resolution analysis of the low-frequency activity in LDF signals was performed for the first time.

Laser-Doppler measurements of BF have previously been performed in experimental and human tumors (6, 18). The overall findings were that BF fluctuates greatly in tumors at frequencies of several cycles per hour and that the changes are heterogeneous, even within the same tumor. We have previously noted this instability in our own laboratory using the Oxford Doppler Array system, and this is demonstrated again in the present study (Fig. 3A). In that example, BF could fluctuate by as much as 40-50% of the average value. Such results are very consistent with other LDF measurements made in tumors (6, 18).

The muscle BF also fluctuated at very low frequencies in these studies. Kvernebo and co-workers (27) measured LDF in human skeletal muscle and made no mention of vasoactive fluctuations in the signals. The examples shown in that study give no evidence of flow motion occurring under control conditions. In a series of studies examining LDF in rabbit skeletal muscle, Schmidt and co-workers (37, 38) demonstrated no slow wave flow motion (1-3 cycles/min) under normal conditions, but occasionally found some higher frequency fluctuations. Thus the lack of typical flow motion activity in the muscle LDF recordings in the present study are in overall agreement with previously published results.

Possible Mechanisms of BF and PO₂ Fluctuations

Vasomotion. The most commonly forwarded explanation for changes in local BF is vasomotion. The rhythmic diameter changes associated with vasomotion typically occur in arterioles below 100 µm in diameter and at frequencies ranging from 1 to 15 cycles/min (7), although this frequency range may be tissue dependent. For example, Hundley and co-workers (22) demonstrated much lower frequencies of vasomotion in cerebral arterioles in awake rabbits. They found the mean frequency of diameter changes to be 0.74 cycles/min, with a range of 0.4-3.5 cycles/min. The nature of vasomotion also changes with vascular diameter. Using a hamster skinfold window preparation, Colantuoni and co-workers (7) found a negative correlation between the fundamental vasomotor frequency and arteriolar diameter and between relative vasomotor amplitude and diameter. Small arteries, with diameters of 70-100 µm, usually fluctuated by 8-30 µm (19% mean amplitude change) at frequencies of 1-3.5 cycles/min (mean of 2.7 cycles/min). Alternatively, terminal arterioles (6- to 15-µm diameter) typically showed rhythmic activity at 6-15 cycles/min (mean of 9.5 cycles/min) with diameter changes of 2-11 µm (89% mean amplitude change).

BF changes via hemodynamic mechanisms. Another possible explanation for the very low-frequency fluctuations seen in this study was put forward by Kiani et al. (25). In a very interesting study (25), they attempted to show the impact of hemodynamic properties on erythrocyte velocity in the microvasculature. They developed a model of network BF based on experimental measurements made in the rat mesentery, and they compared the model results to in vivo measurements of erythrocyte velocity and discharge hematocrit. The model accounted for several hemodynamic characteristics, including nonlinear flow properties of blood, unequal distribution of erythrocytes at vessel bifurcations, and nonuniform axial distribution of erythrocytes within vessels (25). Several significant results came out of the study. First, the model generated temporal variation in erythrocyte velocity and discharge hematocrit with fixed vessel dimensions and constant network flow, indicating that the fluctuations were due solely to hemodynamic factors. Second, vessels arising from the same parent vessel node could demonstrate widely different fluctuation patterns. Third, a Fourier analysis of arteriolar (11- to 48-µm diameter) erythrocyte velocity revealed that the maximal peak frequencies were in the range of 0.05-0.5 Hz (3-30 cycles/min). These patterns of oscillation were similar to those predicted by the model. The observed fluctuations were not caused by vasomotion, because the authors (25) stated that vasomotion was rarely seen in their preparations and they also found these fluctuations when the vessels were maximally dilated.