Heart and Circulatory Physiology

Erythrocyte-associated transients in Po2 revealed in capillaries of rat mesentery

Aleksander S. Golub, Roland N. Pittman


Mathematical models have predicted the existence of Po2 gradients between erythrocytes in capillaries in the usual case where plasma contributes substantial resistance to oxygen diffusion. According to theoretical predictions, these gradients could be detected as rapid Po2 fluctuations (erythrocyte-associated transients, EATs) along the capillary. However, verification of a model and correct choice of its parameters can be made only on the basis of direct experimental measurements. We used phosphorescence quenching microscopy to measure Po2 in 52 capillaries of rat mesentery to obtain plasma Po2 values 100 times/s at a given point along a capillary. A 532-nm laser generated 10-μs pulses of light, concentrated by a ×100 objective, onto a spot 0.9 μm in diameter. The presence of erythrocytes in the excitation region was detected on the basis of phosphorescence amplitude (PA), proportional to the amount of plasma encountered by the laser beam, and on the basis of the intensity of transmitted laser light (LT), detected by a photodiode placed under the capillary. The data revealed correlated waveforms in PA, LT, and Po2 in capillaries. The magnitude of the Po2 gradients between erythrocytes and plasma was correlated with average capillary Po2. EATs in Po2 were more readily detected in capillaries with relatively low oxygenation. The correlation coefficients between PA and Po2 for the half of the capillaries (n = 26) below the median Po2 (mean Po2 = 17 mmHg; R = −0.72) was higher than that for the other half (mean Po2 = 39 mmHg; R = −0.38). These results support the theoretical predictions of EATs and plasma Po2 gradients in capillaries.

  • microcirculation
  • red blood cells
  • oxygen transport
  • oxygen tension gradients
  • phosphorescence quenching microscopy

the effects of the particulate nature of blood flow in capillaries on oxygen transport from red blood cells (RBCs) to tissue have previously been studied solely by mathematical modeling. Hellums (8) simulated capillary oxygen transport by considering the discrete nature of capillary blood flow and made the prediction of a significantly lower rate of oxygen transport compared with a classic homogeneous flow model. Two equivalent approaches to describing the heterogeneity of Po2 in a capillary have been followed, depending on the choice of reference frame. They use different terminology and mathematical presentations for the same phenomenon of oxygen transport from RBC to tissue.

The term “erythrocyte-associated transients” (EATs) proposed by Hellums and coworkers (8, 9) denotes the variations of Po2 at a fixed position along a capillary caused by the alternate passage of individual RBCs and plasma gaps. This definition allows one to distinguish rapid variations of Po2 at a given location along a capillary from Po2 variations caused by oscillations in blood flow, variations of oxygen content in arteriolar blood, or random changes in capillary hematocrit, for example. This approach appears to be effective for describing experimental measurements of Po2 heterogeneity in capillaries in terms of amplitude, frequency, and phase.

For the case in which the reference frame is associated with a RBC moving through a capillary, Po2 heterogeneity is described in terms of a Po2 gradient in the plasma between cells (10). This approach has made possible mathematical modeling of inter-RBC Po2 gradients that depend on RBC spacing, oxygen flux at the capillary wall, RBC shape, and wall-to-RBC spatial clearance (13, 7, 9, 13, 18, 29).

The discrete representation of capillary blood flow in theoretical considerations has demonstrated the significant contribution of intracapillary resistance to oxygen transport from RBC to mitochondria, in comparison with traditional continuous and homogeneous models. By considering the rate of RBC deoxygenation measured in vitro, Lawson and Forster (14) had previously concluded that most of the resistance to oxygen diffusion in capillary networks was offered by the tissues outside the capillaries. This conclusion was based on their calculation for skeletal muscle of a Po2 drop between a RBC and the adjacent plasma of <1 mmHg at rest and 4.1 mmHg with a combination of anemia and exercise (14). In contrast, Hellums (8) later predicted that the fraction of the resistance to oxygen transport in capillaries for a discrete model of capillary flow was twice that found for homogeneous models. Furthermore, the cell-to-plasma Po2 difference was found to be substantial in an independent simulation of oxygen transport in capillaries in the presence of severe, acute anemia (10).

The critical RBC separation distance was defined as a threshold for maintaining uniform oxygen flux at a point along a capillary (3). When the plasma gap exceeds a critical distance, the discrete nature of capillary blood flow determines the rate of oxygen transport from RBC to tissue, because the low plasma Po2 becomes limiting for oxygen exchange. Furthermore, the oxygen tension difference between cells and plasma is an important determinant of the oxygen release from a RBC. Simulation of the intracapillary Po2 distribution in the plasma gap between two adjacent RBCs demonstrated that the Po2 in the middle of the gap at maximal oxygen consumption could be <30% of the Po2 around the RBCs, even for a distance between RBCs equal to one RBC length. In the case of oxygen consumption at rest, a separation distance equal to three RBC lengths caused the midgap Po2 to be ∼20% of that near the RBC. These results showed that the particulate nature of capillary blood flow could have a pronounced effect on oxygen transport not only in anemia and maximal exercise but also under normal conditions in a resting muscle.

A mathematical description of oxygen supply to tissue using Krogh's cylinder model predicted differences in Po2 among RBCs, plasma, and tissue that depended on capillary hematocrit (15). Another theoretical study of the particulate nature of capillary flow on oxygen transport resistance predicted that intracapillary resistance, influenced by the discrete nature of blood, comprised up to 70% of the total resistance to oxygen transport to tissue (2, 18). The predicted decrease of oxygen flux out of a capillary depended strongly on the distance between RBCs in the capillary. The magnitude of the Po2 oscillation at the capillary wall under conditions of maximally working muscle was found to be as large as 80 mmHg for stationary RBCs separated by a distance of four cell lengths (7). However, in the case of RBCs moving at a velocity of 4 mm/s (much higher than normal values), the nonuniformity of oxygen flux out of a capillary due to large plasma gaps was found to be unimportant for the tissue oxygen supply.

RBCs become deformed as they pass through a capillary, and their shape was found to be one of the determinants of total resistance to oxygen transport from hemoglobin to mitochondria (29). The maximum amplitude of the Po2 variation from RBC to plasma was predicted to be about 20 mmHg in the case of zero RBC deformation, and this resulted in a decrease of the wall oxygen flux by about fivefold.

The variety of factors influencing Po2 heterogeneity in a capillary includes RBC oxygen content, RBC spacing, wall-to-RBC clearance, RBC shape, cell orientation in flow, and capillary blood velocity and its pulsation. All these factors can affect the oxygen flux from RBC to tissue, acting separately or in concert. The complexity of the intraluminal processes in a capillary stimulates interest in the experimental study of RBC-to-RBC oxygen gradients in a capillary that can be detected in the form of EATs. It was pointed out in a recent review (26) that presently there are no experimental data on RBC-associated transients in capillary Po2.

The main obstacle to the experimental study of oxygen transients and gradients in the microcirculation has been the lack of a noninvasive method of Po2 measurement with high spatial and temporal resolution. Invention of the phosphorescence quenching technique (28, 30) and its application to the in vivo microscopy of microvessels (23, 24) opened new opportunities to study oxygen transport. Further development of phosphorescence microscopy (12, 21, 2325, 27) has brought new knowledge about oxygen transport in a variety of organs. Significant progress toward better temporal and spatial resolution of the method has been made by using a laser for excitation of the phosphorescent probe (22, 27).

We (31) previously reported evidence of Po2 variations in capillaries with the phosphorescence quenching method, but the spatial and temporal resolutions in that study were not sufficient to attribute these variations to EATs. Therefore, the present study was aimed at refining the phosphorescence quenching technique to measure the fast Po2 transients in a capillary and using them to record variations of oxygen tension in mesenteric capillaries.


Phosphorescence microscope.

The experimental setup (see Fig. 1) consisted of an Ortholux microscope (Leitz) configured for epi-illumination. The preparation was observed with a ×100/1.30 Leitz objective used with immersion oil between the objective and Saran film covering the tissue under study.

Fig. 1.

Schematic diagram of phosphorescence microscope for measuring Po2, phosphorescence amplitude (PA), and intensity of transmitted laser light (LT) in a mesenteric capillary. See text for details. PMT, photomultiplier tube; TTL, transistor-transistor logic; CCD, charge-coupled device; ND, neutral density; ADC, analog-to-digital converter.

The excitation illumination was provided by a transistor-transistor logic-modulated diode-pumped steady-state laser (532 nm, 15-mW continuous work power; GMS1-038-15T, Lasermate, Pomona, CA) that generated 100 light pulses/s. In our experiments, a 10-μs laser pulse delivered 60 nJ to a spot 0.9 μm in diameter, yielding an energy density of 94 nJ/μm2. Light pulse energy was measured from the objective with a Lasercheck power meter (Coherent, Auburn, CA). The variation of pulse energy from pulse to pulse, measured by a photomultiplier tube (PMT) recording the pulse train signal reflected from a mirror, was relatively low [coefficient of variation (CV) = 1.6% after a 15-min warm-up period].

A laser beam was reflected by a dichroic mirror (565 DCLP; Chroma Technology, Rockingham, VT) into the objective lens and to the midplane of the microvessel, where the diameter of the beam waist was 0.9 μm. A correction lens between the laser and the microscope was used to adjust the focal plane of the laser light to the midplane of the capillary under observation. Off-axis alignment of the laser beam was used to exclude direct reflection of laser light from optical surfaces in the center of the various lenses. Emitted phosphorescence was collected by the objective and was detected by a PMT (R3896 with high-voltage socket HC123-01; Hamamatsu, Bridgewater, NJ) that provided the linearity required for 12-bit accuracy.

A barrier filter (interference cut-on 650 nm; Thermo Oriel, Stratford, CT) was located in front of the PMT to provide the opportunity of viewing the excitation light spot and microvessels in the same image. A sliding mirror could switch between two fixed positions for imaging with the video camera and phosphorescence registration with the PMT. The image of a microvessel was collected by a charge-coupled device camera (WAT-902B, Watec), displayed on a 5.6-in. monochrome LCD monitor (45M056, Imaging Solutions) and recorded by a VCR (XA-110, Sharp). No direct eyepiece observation was provided in the system to prevent operator exposure to laser light. Capillary diameter was measured on the monitor (WV-5490; Panasonic), using a video recording with a magnification of 0.7 μm/mm. The excitation spot was placed at the center of the monitor, using a metal mirror in place of the object. During an experiment, its position was checked by focusing on the surface of the Saran film that covered the tissue.

The signal from the PMT was directed to amplifier A (Fig. 1) and then to a 12-bit analog-to-digital converter (PC-MIO-16E-4; National Instruments, Austin, TX). Digitized data were stored and processed in an OptiPlex GX400 computer (Dell; Round Rock, TX). Amplifier A functioned as a current-to-voltage converter made from a precision operational amplifier (OP37EP; Analog Devices, Norwood, MA) with a “disable” function realized by a precision analog switch (ADG419BN; Analog Devices). The pulse generator produced a train of pulses with 10-μs duration and 100-Hz frequency. Each pulse evoked a laser light pulse of the same duration and also disabled amplifier A for that time. Thus each phosphorescence decay curve was recorded from the end of the excitation light pulse to the moment when it reached a practical zero for 12-bit quantization. The acquisition of an unabridged decay curve is a strict requirement for accurate exponential analysis (11).

The 12-bit resolution analog-to-digital converter was controlled by the program “DualGetCurve” written in LabVIEW (National Instruments). The program allows the acquisition of simultaneous data flows from two inputs at a sampling rate of 200 kHz and 400 data points per curve as well as 100 curves in the sequence. The acquired data set was exported to a worksheet in Origin 7.0 (OriginLab, Northampton, MA) for subsequent analysis.

A Po2 measurement rate of 100 Hz was chosen to detect 50-Hz variations in Po2 as estimated by Hellums (8). In recent studies, the RBC flux in capillaries of resting spinotrapezius muscle was found to be in the range of 22–41 RBC/s (19, 20). Therefore, 100 measurements of Po2 per second can be considered a requirement for the time resolution of the method.

We used signal-to-noise ratio (SNR) = 100 as an estimate for the desirable accuracy of digitization (12 bit minimal requirement), so that the estimated decay curve duration should be at least 4.6 τ (11), where τ is the lifetime of the phosphorescence decay. The Pd-porphyrin phosphorescent probe, conjugated with BSA, has a maximal lifetime of τo = 546 μs when Po2 = 0 mmHg (31), so the required duration of the decay curve is 2,500 μs.

The construction of the thermostatic animal platform for intravital microscopy has been described previously (4). The mesenteric tissue was spread over a thermostabilized sapphire window that allowed detection of the laser light passing through the capillary with a T-5 photodiode (Intor; Socorro, NM), integrated with a 532-nm laser line filter (Fig. 1). The photometric signal from the T-5 diode was converted to a voltage with amplifier B and directed to the second channel of the analog-to-digital converter. Therefore, the train of excitation light pulses evoked a train of phosphorescence decay curves and a train of transmitted light pulses, recorded simultaneously to detect the presence or absence of a RBC in the excitation volume at the moment of the Po2 measurement. Both signals were monitored with an oscilloscope (72–3060; Tenma, Springboro, OH).

Selection of a capillary for measurement, positioning of the laser spot, and video recording were performed under transillumination with an OG-570 filter (Edmund Optics, Barrington, NJ). All Po2 measurements were carried out in a dark room to minimize the stray light noise.

Phosphorescent probe.

The oxygen-sensitive phosphorescent probe palladium meso-tetra-(4-carboxyphenyl)-porphyrin (Pd-MTCPP) was obtained from Oxygen Enterprises (Philadelphia, PA). Preparation of 20 ml of the 10 mg/ml probe solution required 200 mg of Pd-MTCPP and 1.2 g of BSA (fraction V; Sigma, St. Louis, MO). Polyvinylpyrrolidone (PVP; mol wt 55,000) was purchased from Aldrich (Milwaukee, WI) and dialysis equipment and Spectra/Por-4 dialysis membrane (molecular weight cutoff: 12–14,000) from Spectrum Laboratories (Campton, CA).

A 100 mM carbonate-bicarbonate buffer (CBB; C-3041, Sigma; pH = 9.6) was prepared, and BSA was then dissolved in 20 ml of CBB by adding 1.2 g in small portions to the well-stirred buffer. Next, 200 mg of powdered Pd-MTCPP were added in the same way but with a cover to protect it from room light. The solution was then transferred into three 10-cm lengths of Spectra/Por-4 dialysis tubing and placed in 1 liter of dialysis solution for 18 h at 4°C in the dark, to remove all unbound Pd-MTCPP that might leak from a capillary and to replace the CBB with PBS. The dialysis solution was prepared from 1 liter of PBS (P-3813, Sigma; 10 mM PBS containing 138 mM NaCl and 2.7 mM KCl; pH 7.4), with 50 g of PVP added to balance the colloid osmotic pressure. We used dialysis as the final step in the preparation of the probe to replace the buffer and remove low-molecular-weight phosphorescent components from the probe.

After dialysis, the probe solution was centrifuged for 10 min at 4,000 rpm and then sterilized by filtration with a 0.2-μm filter unit (Nalgene, Rochester, NY). Aliquots (0.5 ml) of the probe solution were placed in plastic microtubes, quickly frozen, and stored at −20°C. The frozen solution in the microtube was thawed at room temperature and then injected intravenously in an amount necessary to yield a Pd-MTCPP concentration in plasma of 0.5 mg/ml.

Oxygen consumption by the phosphorescence quenching method was tested with venous blood taken from the jugular catheter and placed in a microslide with a 40-μm path length (Vitro Dynamics, Rockaway, NJ). We used a direct method of measuring the Po2 drop from flash to flash by the analysis of individual phosphorescence decay curves. Excitation conditions were the same as in the in vivo experiments except that the blood sample in the microslide remained motionless in order for oxygen depletion to accumulate from flash to flash. Results show that in the Po2 interval of 60–25 mmHg, the Po2 decrease in stationary blood was 1.2 ± 0.6 mmHg/flash (n = 23). It was significantly higher than the oxygen depletion caused by a conventional flash lamp (16, 25) but was small enough to detect the predicted magnitude of EATs of tens of millimeters of mercury. In flowing blood the next flash excites a new portion of dissolved probe, so the Po2 drop of 1.2 mmHg should be identical in all excited volumes of plasma (a new volume with each excitation pulse). No systematic downward trend, which would indicate the accumulated depletion of oxygen in a capillary, was observed in the entire set of capillaries in the mesentery over the 1-s measurement time interval.

Analysis of phosphorescence decay curve.

Individual phosphorescence decay curves (i.e., 1 flash yields 1 curve for analysis) were analyzed with the Origin 7.0 (OriginLab) nonlinear least-squares fitting procedure, using the rectangular model of Po2 distribution published previously (6). The fitting equation was: Math where t (μs) is the time from the beginning of phosphorescence decay, I(t) (V) is the magnitude of the phosphorescence signal at time t, I(0) (V) is the amplitude of the phosphorescence signal at t = 0, M (mmHg) is the mean Po2, δ (mmHg) is the half-width of the Po2 distribution, T (μs) is the lifetime of the fast postexcitation transient, A (V) is the amplitude of the fast postexcitation transient, and B (V) is the baseline offset. The constants Ko = 18.3 × 10−4 μs−1 and Kq = 3.06 × 10−4 μs−1·mmHg−1 were determined in separate calibration experiments (31), where Ko is the phosphorescence decay in the absence of oxygen and Ko is the quenching constant in the Stern-Volmer equation.

The first term in the above equation represents the phosphorescence decay curve for an excitation volume with heterogeneous Po2, dependent on two parameters, M and δ, recovered from the fitting procedure. The second term represents the fast transient component; it was always shorter than 10 μs and could be easily separated from the Po2-dependent signal (shortest τ = 31 μs at 100 mmHg) by the methods of exponential analysis. The fast transient lifetime T and baseline voltage offset B remained constant during the 1-s measurement period. They could be determined accurately from the average curve (100 curves) and were used as constants in fitting the individual curves.

RBC and plasma detection

The detected variation of the local capillary Po2 could be recognized as an EAT only if the magnitude of these variations exceeded the level of experimental noise, and the Po2 changes were supported by simultaneous and independent data on the presence or absence of RBCs in the detection volume. To establish conformity between fluctuations of Po2 and the presence of a RBC or plasma gap in the detection volume, one needs a technique of simultaneous registration of the phosphorescence decay curve and information about erythrocyte or plasma location. Synchronous imaging, combined with phosphorescence measurements at excitation rates of 100 Hz and higher, represents a serious technical challenge. A simpler method was employed, using the registration of the intensity of a laser pulse that passes through a capillary (light transmittance, LT).

Another opportunity to distinguish between RBCs and plasma comes from the analysis of the maximum phosphorescence amplitude (PA) measured at the beginning of a decay curve after the end of the excitation pulse. Because the phosphorescence probe is uniformly dissolved in plasma and never enters a RBC, the maximum amplitude of the phosphorescence signal is proportional to the amount of plasma in the detection volume. To demonstrate that principle, the phosphorescence image of a capillary (Fig. 2A) was made with the same filter set after the probe injection. The densitometric scan (Fig. 2B) along the line drawn in Fig. 2A demonstrates that the intensity of phosphorescence at a point along the capillary can be used to detect the presence or absence of a RBC. Vessels were imaged under ×40 magnification (Axioplan-2; Zeiss) with a CoolSnap cf digital camera (Roper Scientific, Trenton, NJ), and the image was analyzed with the Scion Image program (Scion, Frederick, MD).

Fig. 2.

A: phosphorescence image of a capillary in rat mesentery. Palladium meso-tetra-(4-carboxyphenyl)-porphyrin (Pd-MTCPP) + BSA conjugate was dissolved in plasma at a concentration of ∼ 0.5 mg/ml. Image was obtained with Zeiss Axioplan-2 fluorescence microscope using a ×40 objective and a CoolSnap cf digital camera. Red blood cells (RBCs) appear as dark spots because they contain no phosphor. Bar = 5 μm. B: photometric profile made along the line drawn on the capillary in A. Phosphorescence intensities are expressed as percentages of the maximal value. The depression in phosphorescence intensity between plasma gap and RBC regions of capillary reaches ∼60%.

The Po2 dependence of the PA is insignificant for short light pulses [e.g., for a 10-μs pulse the Po2-dependent change in amplitude is 0.14%/mmHg (5)]. So, even if the EAT is as high as 10 mmHg, the Po2-associated addition to the PA will be 1.4%. Because the expected variation of the PA caused by the presence of a RBC in the detection volume is several tens of percent, the PA can also be used for RBC localization in respect to the region of the Po2 measurement. Thus a negative correlation (in a 100-data point sequence for 1 s) between Po2 and LT or PA can be taken as direct evidence of EAT detection.

To diminish the noise contribution, the amplitudes of the phosphorescence decay curves (PA) and transmittance (LT) pulses were taken as the average of the three highest points at the peak of each signal. The random noise in values of LT, PA, and Po2 was reduced by filtering the signal with a fast Fourier transform filter (Origin 7.0; OriginLab). The sampling rate in our experiments was 100 Hz, so the maximum cutoff frequency was 50 Hz and the minimum was 20 Hz. The first value corresponds to the estimate of Hellums (8) and the second to RBC flux data of 22 Hz (19). For statistical analysis we used unfiltered data. We applied 50-Hz and 20-Hz cutoff frequency filtering to smooth the data presented in graphic illustrations (see Figs. 57).

Variation of the laser pulse energy (CV = 1.6%) was not the only source of fluctuation in the system consisting of the measurement setup and the observed capillary. The intrinsic noise in the Po2 signal was determined on the basis of the Po2 record in a 56-μm diameter venule, where the Po2 was more homogeneous than in a capillary. The Po2 in the venule, averaged for 1 s, was 38.5 ± 0.1 mmHg, with a CV of 2.7%. Filtering the Po2 time series at 50 Hz reduced the CV to 1.9%, and filtering at 20 Hz reduced CV to 1.2%. These results provide reference values to aid in the interpretation of the capillary data: significantly higher levels of CV for Po2 measurements, correlated with LT and PA data, indicate EATs in oxygen.

Animal preparation.

Animal use was in accord with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and was approved by the Institutional Animal Care and Use Committee of Virginia Commonwealth University. Male Sprague-Dawley rats (n = 6; 300 ± 10 g body wt; Harlan Sprague Dawley) were anesthetized with pentobarbital sodium (65 mg/kg ip). Atropine (50 μg/kg) was injected subcutaneously. The left jugular vein was cannulated for injection of the oxygen probe and supplemental anesthetic. The trachea was cannulated to ensure a patent airway, and the animal breathed room air spontaneously. The animal was placed on the heating pad of a thermostabilized animal platform (4), and a loop of intestine was exposed via a medial incision. The mesentery was then spread over a sapphire window and maintained at 37°C. The gut was then gently fixed to a balcony surrounding the window with several overlapping sutures without tissue damage. The mesentery and gut were covered with Saran film to prevent tissue desiccation and to isolate the mesentery from room air and immersion oil.

Experimental procedure.

The Po2 measurements started immediately after injection of the probe. Most capillaries (48 of 52) were measured within 47 min after probe injection; the other 4 were measured within 68 min. This time window for measurements was based on published observations that extravasation of the phosphorescent probe over 35 min of perfusion was insufficient to yield a detectable phosphorescence signal in skeletal muscle (17). To minimize the impact of the extravascular signal on the capillary measurements, the phosphorescence amplitude in the tissue was checked at a distance of ∼20 μm (3–4 diameters) away from a selected capillary. Measurements were not made if tissue phosphorescence was >10% of the capillary signal.

For each capillary, 100 decay curves and 100 transmittance pulses were recorded simultaneously for a 1-s time interval. Each decay curve was sampled at 5-μs intervals for the 4-ms curve duration.


Statistical calculations were made with the program Origin 7.0 (OriginLab). All data presented in Tables 1 and 2 are means ± SE for the number of capillaries indicated, and differences of two means were analyzed with an unpaired t-test. All compared means were significantly different at the P = 0.05 level.

View this table:
Table 1.

Results of measurements in mesenteric capillaries

View this table:
Table 2.

Comparison between two groups of capillaries with high and low Po2


An example of an individual decay curve recorded in a rat mesenteric capillary (7 μm in diameter) is displayed in Fig. 3. The SNR in this curve was 94, sufficient for accurate recovery of the mean Po2 in the volume of detection. Figure 3B shows the same curve in a semilogarithmic plot, to demonstrate the presence of the fast transient (T = 8 μs) at the beginning of the curve and the positive offset. A mean Po2 of 5.6 mmHg was recovered from the analysis of this curve.

Fig. 3.

A: example of an individual (not averaged) phosphorescence decay curve recorded in a 7-μm-diameter capillary in rat mesentery. Points are phosphorescence intensity values taken every 5 μs over a 4-ms period; line is the best-fit curve. B: same data as in A in semilogarithmic plot, to demonstrate the fast initial transient [transient lifetime (T) = 8 μs] and 15-mV positive baseline offset. AU, arbitrary units.

Significant fluctuations of Po2 were measured at a point along a mesenteric capillary during 1 s of 100-Hz flash excitation. Figure 4A shows the Po2 changes in two series of 1-s measurements made in the same capillary (5 μm in diameter) and combined into one data set to obtain a smooth histogram of the Po2 distribution in a capillary (Fig. 4B). Although the Po2 peaks reached 25–30 mmHg, more than half of the Po2 values fell into the 5- to 10-mmHg interval, so that the mean Po2 was relatively low (11.5 ± 0.4 mmHg). The Po2 distributions were different for each data set, but domination by low Po2 values was a common feature for all sets.

Fig. 4.

A: Po2 changes in 2 series of 1-s measurements made in the same capillary (5-μm diameter). B: data were combined into 1 data set (n = 200) to obtain a histogram of Po2 specific for that capillary. Unfiltered data were used for statistical analysis. The Po2 distribution is asymmetric, with most values in the lowest bin (mean Po2 = 11.5 ± 0.4 mmHg).

An example of simultaneous records containing 100 consecutive points for measurements of Po2, PA, and LT made in a capillary for 1 s is shown in Fig. 5. As expected, temporal variations of Po2 appear to be inversely related to those of PA and LT. The PA and LT signals changed in parallel, and both of these signals can provide information on the presence or absence of a RBC in the detection volume for comparison with the Po2 time course. Signals measured in the 5-μm-diameter capillary presented in Fig. 5 were filtered with the 20-Hz cutoff frequency. The Po2 variations were found to be ∼10–15 mmHg. Each peak on the Po2 chart had a corresponding trough in the PA and LT records. The distance between peaks was in the range of 125–185 ms (corresponding to a cell flux of 5–8 cells/s), and a plasma gap detected in the first half of the measurement period was ∼450 ms long. Another record, presented in Fig. 6, has a more complex shape that can be interpreted as being due to overlapping RBCs in a 7-μm-diameter capillary. The changes in amplitude of the Po2 curve are opposite in direction to those of the PA and LT curves. We could not estimate the RBC flux in all 52 capillaries. Even in the one-third of the capillaries where distinct EATs were observed, it was difficult to distinguish with certainty between individual or overlapped cells. In other capillaries the presence of EATs was diagnosed on the basis of correlations between the independent signals, modulated by RBC passage, but having no distinct RBC peaks.

Fig. 5.

Example of simultaneous records containing 100 consecutive points for measurements of Po2, PA, and LT made in a capillary (5-μm diameter). Signals were filtered with 20-Hz cutoff frequency low-pass filter. Vertical dashed lines designate the RBC passage through the detection volume. Temporal variations of capillary Po2 are inversely related to changes in PA and LT. PA and LT change in parallel in response to RBC passage. Plasma gap detected in the first part of the measurement period was ∼450 ms long; RBC peak duration ranges from 125 to 185 ms. Mean Po2 difference between 9 adjacent midcell and midgap regions was 10.1 ± 1.2 mmHg.

Fig. 6.

Simultaneous records of Po2, PA and LT (20-Hz cutoff frequency filtering) made in 7-μm-diameter mesenteric capillary. PA and LT curves change in parallel and oppositely from Po2 change. Po2 transients related to passage of individual RBCs are not as distinct as those in Fig. 5.

The paired correlation coefficients for all three signals can be used to demonstrate that the detected Po2 changes can be recognized as EATs. The signals presented in Fig. 7A underwent minimal filtering (50-Hz cutoff). The Po2 data have a high negative correlation with the LT (−0.71; Fig. 7B) and PA (−0.88; Fig. 7C) signals. The correlation between LT and PA is positive (0.72; Fig. 7D), and that can be explained by the similar nature of both signals: presence of a RBC in the excitation volume reduces both transmitted (hemoglobin absorption) and emitted light (less plasma containing phosphor).

Fig. 7.

A: time courses of Po2, PA, and LT in a capillary, smoothed with 50-Hz low-pass filter, presented in a semilogarithmic plot. B–D: paired correlations of the 3 signals. Significant negative correlations were found between Po2 and LT (R = −0.71, P < 0.0001; B) and between Po2 and PA (R = −0.88, P < 0.0001; C). Parallelism between PA and LT was demonstrated by a positive correlation coefficient (R = 0.72, P < 0.0001; D).

The distributions of the correlation coefficients for the total set of capillaries are displayed in Fig. 8. A negative correlation between Po2 and PA (Fig. 8A) was found in 88% of the measurements, making PA the best indicator of RBC presence in the detection volume. A positive correlation between LT and PA (Fig. 8B) was found in 65% of the capillaries, and a negative correlation between LT and Po2 (Fig. 8C) was found in 56% of the capillaries.

Fig. 8.

Paired correlation coefficients for the 3 signals. A: correlation coefficients between Po2 and PA were negative for 88% of the 52 capillaries. B: LT was positively correlated with PA in 65% of the capillaries. C: LT was negatively correlated with Po2 in 56% of the capillaries.

The CV for capillary Po2 in all capillaries was not less than 5%, and the mean CV was 17.6% (see Table 1), much higher than the 2.7% related to the method itself. More than 60% of the capillaries had a CV >10% (histogram in Fig. 9), indicating that in most capillaries Po2 fluctuated significantly during the 1-s measurement period. For many capillaries these changes appear as a series of EATs, with distinct peaks and troughs corresponding to the passage of single RBCs and plasma gaps, respectively, as occur in mathematical models of discrete blood flow in capillaries. In other capillaries, the Po2 fluctuations are less distinct and most likely correspond to the alternate passage of trains of RBCs separated by short plasma gaps, with slower trends that are possibly associated with variations in blood velocity or capillary hematocrit. However, the CV of capillary Po2 showed a close relation with the correlation coefficient between Po2 and PA, R(Po2/PA), a good indicator of EATs: the capillaries that exhibited a high negative R(Po2/PA) also had a high CV of capillary Po2 (see correlation in Fig. 10).

Fig. 9.

Coefficient of variation (CV) for Po2 in all measured capillaries. Mean CV was 17.6 ± 1.5%. All 52 capillaries had CV >5%, indicating that rapid Po2 fluctuations are common in mesenteric capillaries.

Fig. 10.

Correlation coefficient between Po2 and PA R(Po2/PA) vs. CV of Po2. R(Po2/PA) indicates the dependence of Po2 on presence or absence of RBC at the measurement site, whereas the CV of Po2 is an indicator of the magnitude of the Po2 fluctuations. The significant correlation between these 2 parameters demonstrates that the same capillaries with higher Po2 fluctuations had high negative correlation coefficients, indicating the presence of erythrocyte-associated transients and that RBC passage is the main cause of Po2 fluctuations in capillaries.

The frequency and magnitude of EATs depend on the interplay between different metabolic and hemodynamic variables that result in the average Po2 in the capillary. The comparison between two groups of capillaries with high and low average Po2 (52 capillaries divided about the median Po2 into 2 distinct groups of 26) showed that the low-Po2 group had a significantly higher CV and negative correlation between Po2 and PA (see Table 2), indicating the much more pronounced EATs in capillaries with low oxygen levels.


Theoretical models that take into account the discrete nature of blood flow in capillaries have predicted the existence of substantial Po2 gradients in the plasma between adjacent RBCs. We have presented the first experimental evidence to support this prediction in the form of EATs in plasma Po2. The demonstration of EATs required the use of a technique with sufficient spatial and temporal resolution to register rapid fluctuations in plasma Po2 at the capillary level and used pulsed laser excitation of a phosphorescent probe confined to the plasma. In addition, it was necessary to be able to distinguish between the presence of a RBC and plasma. This was done by utilizing the intrinsic properties, respectively, of RBCs to absorb light (LT measurement) and the excited phosphor probe in plasma to emit light (PA measurement). The magnitude of these signals was related in a quantitative way to the amount of hemoglobin or plasma, respectively, in the detection volume. The observed frequency of Po2 fluctuations corresponded to the expected RBC flux in capillaries, and the depth of modulation of Po2 (10–15 mmHg) corresponded to the predictions of the theoretical models of discrete flow in capillaries.

Application of the 532-nm pulsed laser to oxygen probe excitation in phosphorescence quenching microscopy provided a substantial gain in the sensitivity, as well as spatial and temporal resolution, of Po2 measurements. The use of an oil-immersion objective with high magnification and high numerical aperture also improved the sensitivity of the instrumentation and its ability to localize the signal. The noise in the Po2 measurements for 1 s had a CV <3%, making it possible to recognize Po2 variations in a capillary that had significantly higher CV, which could be used as an indicator of Po2 transients in the detection volume.

The above advances in instrumentation made possible the direct detection and recording of the variation of Po2 in the plasma flowing through a capillary at an observation point along the vessel. Data showing the variation of Po2 were corroborated with simultaneous records of the PA and LT signals, taken at the same point in the capillary. Correlations between Po2 variation and changes in PA and LT represent strong supportive evidence for the presence or absence of a RBC in the detection volume at the moment of measurement. PA was a better indicator of the presence of a RBC or plasma than LT, probably because of the complex refraction of transmitted light by a RBC with a random orientation and technical problems related to the alignment of the photodiode placed under the tissue.

The displays of Po2 and the two optical signals vs. time demonstrated a variety of types of Po2 transients. In many capillaries the variation of Po2 was related to the passage of individual RBCs, identified as EATs with single distinct peaks. There were also complex peaks, presumably formed by the passage of RBC trains and plasma gaps. This interpretation of the Po2 time course was based on simultaneous recordings of LT and PA. In some capillaries small positive or negative trends and slow waves in Po2 were noted. These could be associated with temporal variations of blood velocity and hematocrit in the capillary.

The depth of Po2 modulation by RBC passage was found to be associated with average capillary Po2 for the 1-s observation period. EATs in mesenteric capillaries were more prominent in capillaries with low average Po2. Those capillaries also had a higher CV of Po2 and a substantial negative correlation between Po2 and PA.

Capillaries with small or undetected EATs were usually characterized by high average Po2, possibly due to higher blood velocity or higher local hematocrit. Therefore, it is possible that the temporal resolution of 10 ms was not high enough to measure these EATs. If the small temporal variation of capillary Po2 is a result of low oxygen consumption by the mesenteric tissue, then organs with a higher metabolic rate, such as brain or contracting heart and skeletal muscle, may have EATs even at high RBC velocity. The search for EATs in tissues with high capillary blood flow and high oxygen consumption should be performed with a Po2 measurement rate higher than the 100 Hz used in the present experiments.

It is of interest to consider the impact of photooxidation after probe excitation on the EATs. The maximum depletion of oxygen that accumulates during the decay of the excited Pd-MTCPP after an excitation flash corresponds to a 1.2-mmHg drop in Po2. We argued earlier that the fall of Po2 in the plasma due to photooxidation should be the same near and far from a RBC (the time course of phosphorescence decay is rapid and faster than the time required for release of oxygen from hemoglobin in the RBC), so that the depletion of oxygen should have an equal impact at each time point in the 1-s measuring period. It is unlikely that the deep modulation of Po2 in some capillaries with distinct peaks and troughs (about one-third of the total) is due to photooxidative oxygen depletion, because all capillaries should exhibit that same behavior if this is the cause, and most of the capillaries have more subtle modulation of Po2 that can be confirmed only by statistical evaluation (i.e., correlation of Po2 with signals representing the presence of plasma or RBCs). We observed that capillaries with higher mean Po2 have lower modulation of Po2 (see Table 2); however, this is the opposite of what one would expect if photooxidation were responsible for the modulation, because the degree of oxygen depletion by this mechanism is proportional to Po2. Finally, other than the passage of RBCs, there are no obvious sources of fluctuations that would modulate the capillary Po2 at ∼10 Hz.

EATs, fluctuations in the time course of Po2 as alternate RBC and plasma regions sweep past the measurement site, are a time-encoded record of the spatial Po2 gradient. The transformation between the time course and longitudinal spatial gradient requires knowledge of the velocities of individual RBCs as they pass the measurement site. Unfortunately, we were not able to obtain those data simultaneously with the Po2 measurements, and thus it is difficult to judge the spatial dependence of the gradient. However, despite our lack of knowledge of the spatial gradient, we can predict that the depth of the gradient depends on the local oxygen consumption of the tissue and the separation between adjacent RBCs, among other things. In Fig. 4, the rate of fall of Po2 away from a RBC is consistently steep, suggesting that the steepness of the Po2 gradient away from a RBC is similar for the RBCs passing the measurement site during this brief period. There are some peaks in Po2 where the falloff is not as steep; presumably these correspond to RBCs that are more closely spaced. The relatively flat Po2 “gradient” between 1.2 and 1.4 s likely reflects a limit on the rate of oxygen diffusion from that large plasma gap, due to the small Po2 difference between plasma and nearby interstitial fluid. A definitive interpretation of EAT data in terms of a longitudinal spatial Po2 gradient in a capillary awaits further technical developments that will allow simultaneous measurements of RBC velocity and spacing.

The finding of EATs in mesenteric capillaries gives strong support to theoretical concepts and predictions developed in mathematical modeling studies, as mentioned in the introduction (2, 3, 710, 18, 29). The predicted magnitude of EATs in capillaries of resting tissue has maximal values around 10 mmHg (13, 29) for the typical cell separation distance and oxygen content of RBC, which is quite consistent with obtained results. CVs of the Po2 distribution at the capillary wall, calculated for the model with an oxygen flux boundary condition and different intererythrocytic gap length, yielded a maximal CV of 52% for stationary RBCs and 24% for RBCs moving at 4 mm/s (7). The experimentally obtained CV for 52 capillaries (see Fig. 9) is distributed in the range of 5–52%, indicating the suitability of the stationary model for mesenteric capillaries. The distribution of CV for capillary Po2 (Fig. 9), compared with the prediction of the stationary RBC model for a given separation distance, indicates that 32 capillaries (of 52) had an RBC separation distance of <1 cell length, 18 capillaries had a separation distance between 1 and 2 cell lengths, and only 2 had a separation distance of ∼4 cell lengths. These comparisons demonstrate the general consistency between the experimental data and one of the mathematical models, which lends support to the validity of its concept and boundary conditions.

The existence of EATs indicates a significant resistance to oxygen transport in the blood. This resistance is contributed primarily by the low solubility of oxygen in the plasma, and it increases when the separation between RBCs increases (i.e., decreased hematocrit). This phenomenon, most strongly expressed at low capillary Po2, can limit the oxygen supply to tissue in hemorrhage, hemodilution, different types of anemia, and intense exercise. In hemorrhage, this effect must negatively influence oxygen transport, creating a transport limitation even when RBC oxygenation is normal. The demonstration of EATs in capillaries provides two roles for capillary hematocrit in determining oxygen transport. A reduction of capillary hematocrit not only causes a decrease of convective oxygen delivery into capillaries but, in addition, increases the EAT-related diffusion resistance for oxygen transport from capillary to tissue.

These results also provide a different view of the function of oxygen-carrying blood substitutes, having comparatively low oxygen content but distributed in the plasma space. Even by making a small contribution to the oxygen capacity of blood during hemorrhage, they may decrease the capillary resistance to oxygen transport by increasing oxygen solubility in the plasma, thereby damping the EATs.

In conclusion, using laser pulse excitation, immersion optics, and a 100-Hz measuring rate of Po2 in capillaries, we have found the theoretically predicted EATs in capillary Po2 experimentally in mesenteric capillaries of rats. The EATs were most pronounced in capillaries having low average Po2. The association of the Po2 variations with the passage of a RBC or plasma gap across the detection volume was corroborated by simultaneously recorded data on PA and LT at 532 nm. The direct testing of the theoretical models of discrete capillary blood flow has bolstered the predictions of EATs and inter-RBC gradients of Po2, supporting the hypothesis of a significant plasma resistance to oxygen transport to tissue, especially under conditions of hypoxia and hemorrhage.


This work was supported by National Heart, Lung, and Blood Institute Grant HL-18292.


We thank Michael L. Fulk for writing the “DualGetCurve” program.


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