INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

PREVIOUS STUDIES of blood flow in small tubes in vitro (4, 19) and in microvessels in vivo (28) yielded conflicting results with respect to the flow resistance. The reported apparent viscosities were higher in living microvessels than in glass tubes of comparable size (8, 12, 18). This raises the question of which rheological mechanisms add to the high flow resistance observed in vivo.

Available studies suggest that a large part of the observed in vivo/in vitro discrepancy may be related to the special nature of the endothelial surface: The inner vessel surface is covered with an endothelial surface layer (7), which was suggested to have a thickness of 0.5-1 µm based on experimental measurements in microcirculatory vessels (7, 23, 30). The importance of this layer for the microvascular flow resistance has been shown by theoretical analysis (6) and direct determinations of flow resistance in vivo (23). However, these studies indicate that such an endothelial surface layer alone may not completely explain the full difference between in vitro and in vivo (23).

Other potential causes for increased flow resistance in vivo are the different composition of the perfusates and the irregular geometry of microvessels. In most in vitro studies not aimed at investigating red blood cell (RBC) aggregation, erythrocytes resuspended in physiological salt solution were used. As a consequence, plasma constituents that may promote aggregation were substantially diluted (if present at all). In contrast, the known aggregation tendency of RBCs in plasma or in whole blood (1, 24) may enhance the formation of clusters of RBCs in the flowing blood stream. An additional obvious characteristic of the in vivo situation compared with in vitro models entailing long, straight glass tubes is the irregular geometry of microvascular networks. Irregularly shaped vessels show substantial changes of diameters with length (5, 11, 20), leading to distortion and breakup of flowing RBC clusters. These effects may cause dissipation of energy and could thus contribute to the total flow resistance. In addition, at diverging bifurcations, RBCs are distributed to the daughter branches separating clustered RBCs, a process that is also likely to add to the overall energy dissipation. Therefore the present study was aimed at investigating RBC flow patterns in microvessels in vivo.

Whereas the formation of large RBC aggregates in resting blood is easily visible, the detection of the optical patterns created by clustering of RBCs in the flowing blood in microvessels poses a difficult technical problem. Because of the short length of individual microvessels, single high-speed photographs do not contain sufficient information to analyze the RBC flow pattern. Serial exposures entail a discontinuous mixture of spatial and temporal information, rendering analysis very difficult if possible at all. This problem can be avoided by continuous recording of light intensities at a given location within the vessel, as it has been done with two photodetectors to determine in vivo RBC flow (26). Here, such traces have been analyzed to obtain information on RBC flow patterns themselves employing Fourier transformations.

In the present study light intensity traces with a length of ~3 s were recorded at a sampling rate of 10 kHz to allow the interpretation of pattern sizes in the range of 5 to ~100 µm at flow velocities between 0.1 and 40 mm/s. To validate the interpretation of the resulting Fourier spectra, two model approaches were used. On one hand, mechanically moved artificial textures in the focal plane of the intravital microscope were taken instead of the in vivo preparation to generate spectra. On the other hand, simple theoretical spectra with given features were transformed back into corresponding optical patterns. These approaches allow a direct comparison of known pattern properties with features of the resulting spectra and vice versa.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

In vivo procedures. In vivo experiments were conducted in the microvasculature of the rat mesentery using intravital microscopy following the approval of the procedures used by university and governmental committees on animal care. Details of the animal preparation and the setup used for intravital microscopy have been described elsewhere (23). In brief, Wistar rats (300-450 g body wt) of either sex were prepared for intravital microscopy of the mesenteric microcirculation following premedication (atropine 0.1 mg/kg im and pentobarbital sodium 20 mg/kg im), anesthesia (ketamine 100 mg/kg im), cannulation of the trachea, jugular vein, and carotid artery, and abdominal incision along the linea alba. The level of anesthesia and fluid balance were maintained by intravenous infusion of physiological saline (24 ml · kg¹ · h¹) containing 0.3 mg/ml pentobarbital sodium during the experiment of up to 2 h. Heart rate and arterial blood pressure (range 105-140 mmHg) were continuously monitored via the catheter in the carotid artery. After the surgical preparations were completed, the animals were transferred to a special stage mounted on an intravital microscope. The small bowel was exteriorized, and fat-free portions of the mesentery were selected for investigation with a ×25 objective lens/numerical aperature 0.6 salt-water immersion lens (Leitz). A Newport MX510 micromanipulator was used for microocclusions of the observed vessels with a glass microrod. In some experiments, Dextran T 250 (mol wt 250 kDa, 0.8 g/kg body wt; Carl Roth, Karlsruhe, Germany) was infused intravenously.

Vessel diameters were measured offline from the video recordings of the microscopic image taken during the experiments using an imaging system (16). In brief, a video recorder was connected to a personal computer via a frame-grabbing device. Distances within a frozen image were measured by using a software controlled pointer displayed on a video screen.

Flow velocity measurements and light intensity recordings. Flow velocities were measured using a dual-window method (see Fig. 1). A rotatable pair of photodiodes mounted on an adjustable holder was positioned in front of a screen onto which the microscopic image was projected (17). The holder with the pair of photodiodes was aligned with the axis of the vessel to be investigated. Given the overall magnification of the microscope system, the equivalent center-to-center distance between the two photodiodes was 5.5 µm in the mesenteric plane. The size of the light-sensitive area of each diode was equivalent to a spot of 5 µm in diameter. To allow offline determination of the time delay, the output signals of both photodiodes were amplified, analog-to-digital converted, and sampled at a frequency of 10 kHz with a converter card in a personal computer (15). Recordings of 3.3 s duration (i.e., 33,000 data points for each diode channel) were collected and stored on disk. On the basis of the sampling frequency and the Nyquist theorem, it can be estimated that only events with a duration >0.2 ms can be determined by the system. Taking into account the upper limit of flow velocities in the recorded vessels (20 mm/s, see below), the upper limiting spatial frequency of the system is 1/(0.2 ms · 20 mm/s), or 250 mm¹. Thus flow patterns with a size >4 µm can be recorded at maximal flow velocities, coinciding with the spatial resolution imposed by the size of the photodiodes.

View larger version (75K): [in this window] [in a new window]   Fig. 1.   Experimental setup. Vessel image generated by an intravital microscope is projected onto a screen on which adjustable photodiode pairs are mounted. Amplified signal of both diodes is analog-to-digital (A/D) converted and stored on a personal computer for subsequent processing. Centerline flow velocity is determined by temporal correlation. Power spectra resulting from Fourier transformation (FFT = fast Fourier transform) of light intensity traces are rescaled from temporal to spatial dimension (spatial frequency = pattern length1) using actual velocity.

Velocity was determined by dividing the distance between the two photodiodes within the image through the time delay of corresponding intensity patterns passing the two photodiodes. Values for the time delay were obtained offline by cross-correlating successive sections of the two intensity traces using a fast Fourier transform (FFT) algorithm (2). Data sections starting at regularly spaced (10 ms) offsets were used. The time interval included in a given section was adjusted according to the previously determined flow velocity to correspond with a spatial length of at least 150 µm. The exact length was dictated by the number of data points, which had to be a full power of 2. If the included time interval exceeded the offset of the next section, the individual data sections were allowed to overlap.

Independent calibration measurements using a rotating disk assembly ascertained that the velocity measurement system was accurate within ±5% up to velocities of 50 mm/s. Lower sampling frequencies and longer overall recording times were chosen in cases of slow blood flow (below ~3 mm/s). Pseudoshear rates () were calculated from the average centerline velocities divided by the vessel diameter at the site of velocity recording.

Computation of power spectra. From the collected raw data of the intensity tracings for each diode, power spectra were calculated, including 32,768 (2¹⁵, the FFT algorithm calls for the number of data points to equal a power of 2) data points (indicated as FFT in the flow chart of Fig. 1). At a sampling rate of 10 kHz, this amount of data corresponding to ~3.3 s was found sufficient to recognize typical patterns. The spectra of both diode traces were averaged and converted from the time domain to the spatial domain by dividing through the mean velocity prevalent during the recording period thus yielding plots of spectral power versus spatial frequency (in the literature commonly denoted as "wavenumbers").

Sections of the resulting spectra corresponding to spatial frequencies from 0 to 200 mm¹ (equivalent to spatial lengths from infinite down to 5 µm, including a total number of individual values varying with the actual pattern velocity in a given recording) were chosen. These sections were assigned to arrays with a uniform length of 200 data points by averaging all data points of the original spectrum within 200 equally spaced frequency bins of 1 mm¹. This rescaling and compressing allowed a point-by-point averaging of results from individual experiments in an ordinary spreadsheet program. Double logarithmic representation was chosen for graphic representation to facilitate the interpretation of structural characteristics in the averaged spectra.

Spectra, except those obtained with the regular pattern of a micrometer scale that exhibit a pronounced peak, were fitted to a continuous and smooth function composed of two straight lines linked together with a curved transition zone (cubic spline) by a least-square simplex algorithm (14). The fitted curve was characterized by the following parameters: the slope of each of the straight parts, their common intercept, and the two points where the spline function separates from the respective straight lines, i.e., the lower and upper boundary of the transition zone. For microvessels with the exception of capillaries, the slope of the straight line at low spatial frequencies (high pattern lengths) was found to be close to zero (slope of log-power vs. log-frequency: 0.21 ± 0.59, means ± SD). Therefore, a simplified model assuming a flat portion of the spectrum at low spatial frequencies and a zero slope at the lower boundary (inflection of the cubic function) was used for the respective data reducing the number of fitted parameters from 6 to 4.

All software programs were written in Turbo Pascal 7.1 and Delphi-Pascal 3.1 (Borland International, Scott Valley, CA).

Validation experiments. A micrometer scale with bars at 10-µm distances that moved across the microscope table at constant speed was used to generate a regular periodic pattern, which was recorded and analyzed with the same optical and electronical setup used in the animal experiments (Fig. 2, A and B).

View larger version (61K): [in this window] [in a new window]   Fig. 2.   Validation. A micrometer scale was moved under the microscope with constant speed (0.8 mm/s). A: microscopic image of scale projected on photodiode pair (small dark rectangle in middle of bright circular area). B: signal recorded from one photodiode that has appearance of a regular sine wave (abscissa: time, ordinate: light intensity). C: power spectrum showing a peak that corresponds to frequency of sinusoidal light intensity trace.

Further model experiments employed more irregular artificial textures such as a monolayer of Sephadex beads (diameters ranging from 20 to 80 µm, mean diameter 31 µm, see Fig. 3, A) on a rotatable disk. The device was mounted onto the microscope table, and the tangential speed of the disk at the focus site was set to values from 3 to 30 mm/s. Additional experiments used wet-mount erythrocyte preparations. Human RBCs were washed two times with isotonic saline and suspended to a final hematocrit value of 30%. A drop of this suspension was placed onto a microscope slide and covered with a coverslip (see Fig. 3, B). This arrangement was moved across the microscope table at constant speed. Validation procedures also included measurements of erythrocyte flow through glass capillaries of 28.5 µm in diameter. Human blood was centrifuged for 5 min at 2,000 rpm, and the buffy coat was removed. RBC suspensions in phosphate-buffered saline were adjusted to hematocrit values of 20 and 40%, respectively, and transferred to a 2-ml syringe. The syringe was constantly rotated during the experiment to avoid sedimentation of erythrocytes. From the syringe, RBC suspension was drawn through the capillary at RBC velocities between 0.15 and 5.25 mm/s by applying negative pressures ranging from 2 to 103 cmH₂O at its downstream end.

View larger version (65K): [in this window] [in a new window]   Fig. 3.   Test patterns. A: monolayer of Sephadex beads on a rotating disk (particle size: 20-80 µm, mean 31 µm; n = 28 recordings, velocity 13.7 ± 8.2 mm/s, means ± SD; fitted parameters: intersection point 33.0 µm, lower boundary 17.8 µm, upper boundary 113.3 µm). B: wet-mount preparation of washed and resuspended human red blood cells (RBCs) on a glass slide. Slide was moved across object plane at a constant velocity of 2.5 ± 1.5 mm/s (n = 10, fitted parameters: intersection 9.6 µm, lower boundary 6.6 µm, upper boundary 20.5 µm). In double logarithmic representation, power spectra for both patterns (bottom panels) show two linear regions at high- and low-spatial frequencies joined by an intermediate curved transition zone. In both experiments, the resulting spectra were not affected by velocity of disk or slide, respectively.

In reversing the direction of the analysis, simplified model spectra were converted into two-dimensional images (Fig. 4). Three basic types of power spectra were chosen as models: 1) a spike function with positive power only at a discrete value, 2) a step function with high power at low spatial frequencies and zero power above a certain threshold value, and 3) a function defined by a linear decrease of the logarithm of spectral power with the logarithm of spatial frequency (Fig. 4A). These model functions were rotated around the origin, creating three-dimensional functions resembling 1) a tube, 2) cylinders, and 3) a cone (Fig. 4B). These three-dimensional spectra, combined with a random phase distribution, i.e., equally distributed random numbers between 0 and 2  in the phase domain of a polar presentation of the complex spectra, were back transformed by a two-dimensional FFT algorithm using a program with a 512 × 512 complex data array. The back-transformed functions are represented by two-dimensional images where the function values are represented as gray levels (Fig. 4C) to allow visualization of particular characteristics of the underlying model power spectra; unit of length in this case was the number of pixels, and each image consisted of 512 × 512 pixels.

View larger version (70K): [in this window] [in a new window]   Fig. 4.   Reverse transformation. Power spectra (A, 512 points) entailing simple characteristics such as a single peak (spike), an abrupt edge (step), or a negative slope are expanded to three dimensions by rotating around spectral density axis: spike is transformed into a tube, steps into cylinders, and negative slope into a cone (B). Reverse two-dimensional FFT (with a randomly distributed phase) leads to image patterns shown in C. Tube and cylinder spectra yield images with typical pattern sizes (left and center), cone spectrum generates a cloudy, fractal image.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Validation experiments. The optical pattern generated by the moving micrometer scale yielded a power spectrum with a dominant peak at a spatial frequency of 100 mm¹ [log value 2.0] corresponding to a pattern length of 10 µm (Fig. 2). All other patterns tested did not produce distinct peaks in the power spectrum. In the double logarithmic plot, they could be fitted adequately by two separate straight lines linked with a curved transition. The relevant parameters characterizing these fits (upper and lower boundary of the curved transition zone, intersection of the adjacent straight lines) for the in vivo data are given in Table 1.

A monolayer of Sephadex beads provided the possibility to investigate a known irregular pattern both visually as a two-dimensional image and using the power spectra generated from light intensity traces (Fig. 3A). The beads had a diameter of 30.6 ± 9.3 (means ± SD) µm as measured from video recordings. The regression analysis of the power spectra resulted in an extrapolated intersection at 33 µm with a transition zone from 18 to 113 µm. The wet-mount preparations of erythrocytes (Fig. 3B) showed an intersection at 9.6 µm with a transition zone from 6.6 to 20.5 µm. The above results were independent of the actual velocities of the test patterns.

Reverting simple three-dimensional power spectra into two-dimensional images revealed pattern characteristics depending on the original spectra used (Fig. 4). In case of the tube or cylindrically shaped power spectra, the resulting images (Fig. 4C) could be described as patterns of granules of different brightness but of similar size. The apparent diameter of these granules as pattern elements was in good agreement with the function value of the tube spectrum (Fig. 4, left column) or the upper limiting value of the cylindrical functions (128 pixels for the middle left column and 64 pixels for the middle right column). In contrast, if spectral power decreased continuously with increasing frequency (right column), the resulting image (bottom right panel) did not show an obvious predominant pattern size. The image resembled the surface of broken granite with some fractal characteristics and the lack of a preferential granulation size.

In vivo results. Spectra obtained from blood flowing through microvessels in in vivo experiments exhibited strong similarities to those of the model experiments with Sephadex beads or with wet-mount preparations of erythrocytes. In particular, no obvious peak could be detected in any in vivo spectrum, and these spectra could be adequately fitted by two separate straight parts linked with a curved transition zone. The parameters of the respective fits are summarized in Table 1.

The in vivo experiments were divided into two major groups, one performed under control conditions without any manipulation of the blood flow and the other one including local or systemic intervention to alter the flow conditions in the observed vessels. These manipulations entailed partial local obstruction of blood flow with a glass microrod or systemic infusion of high-molecular-weight dextran (250 kDa mol wt) to alter RBC aggregability and a combination of both treatments. Within each of these sets, power spectra of arterioles and venules were not distinguishable.

Observations in vivo at spontaneous flow conditions. The appearance of the power spectra obtained from in vivo experiments without manipulating the blood flow varied both with vessel size and with shear stress. Averaged spectra (means ± SD) for three different diameter categories are presented in Fig. 5. Common to all spectra was a marked negative slope at the high-frequency end. Except in capillaries, which showed a clear negative slope in the left part of the spectrum comparable to that of the spectra obtained with Sephadex beads or wet-mount preparations, the straight part at lower frequencies was flat (linear fits of that part revealed slope values that were not statistically different from zero). The two linear sections of the spectral curves were linked with a distinct curved transition zone. Both the intersection point of the two straight lines and the upper boundary of the transition zone shifted to higher pattern lengths with increasing vessel diameter. In contrast, the values of the lower limits corresponded to the size of a single RBC for all spectra of flowing blood as well as for those obtained with wet-mount preparations of RBCs (Table 1).

View larger version (29K): [in this window] [in a new window]   Fig. 5.   Power spectra obtained from microvessels at pseudoshear rates (centerline velocities divided by vessel diameter) above 160 s1 for different diameter classes.

Figure 6 gives the dependence of intersection point (I) and upper boundary (B) on vessel diameter and pseudoshear rate. For capillary vessels the values for both parameters remained close to the size of RBC (or the distance between RBC centers in capillary flow) independent of shear rate over the tested range. For pre- and postcapillary vessels, in contrast, the pattern sizes indicated by I and B increased significantly with increasing diameter and pseudoshear rate.

View larger version (31K): [in this window] [in a new window]   Fig. 6.   Effect of vessel diameter (D) and pseudoshear rate () on intersection point (left panels) of fitted straight lines, interpreted to indicate typical pattern length (I) and on upper boundary (right panels) of curved transition zone, indicating maximal pattern length (B) for capillaries () and pre- and postcapillary vessels (). For pre- and postcapillary vessels linear regressions are shown with 95% confidence intervals. Respective equations are the following: I = Log D · 11  3.9, r2 = 0.25; B = Log D · 66.2  55.6, r2 = 0.27; I = Log U · 10.4  11.6, r2 = 0.38; B = Log U · 67.8  114, r2 = 0.25.

To investigate the reproducibility of the method for in vivo measurements, repeated recordings (n = 6) over a time of 6 min were performed at two microvessels (diameter 23 and 28 µm, shear rates 150 and 170 s¹, respectively). If intensity traces from both diodes were analyzed independently without averaging the two spectra of each recording before applying the analysis and fitting procedure, the intercepts differed by 0.32 ± 0.72 µm, or 3.4 ± 7.7% (means ± SD). The intercepts of the six consecutive measurements (spectra of the two diodes averaged) yielded mean values of 9.6 ± 0.76 and 16.4 ± 0.81 µm, respectively, for the two vessels. This corresponds to a percentage deviation of repetitive measurements of 7.9 and 4.9%. These results show that the scatter introduced 1) by the recording and analysis methods and 2) by time-dependent variability of the signal in a given vessel are small compared with the typical biological scatter of >10 µm for data obtained from different vessels with similar shear rates and diameters.

Experimentally altered flow conditions. After treatment with high-molecular-weight dextran and upon local mechanical obstruction of blood flow with a glass microrod, power spectra were observed that exhibit higher pattern length values for the intersection and the lower boundary parameter (Table 1). However, results for altered flow conditions seem to coincide with those for spontaneous flow conditions for a given level of shear rate in the range above ~100 s¹ (Fig. 7). For pseudoshear rates below 100 s¹, increase of the flow pattern size with decreasing shear rate is seen. However, such low rates have mostly been observed for intentionally altered flow conditions.

View larger version (23K): [in this window] [in a new window]   Fig. 7.   Effect of pseudoshear rate on intersection point. Data for spontaneous flow conditions () are compared with results obtained on infusion of dextran (250 kDa mol wt, 0.8 g/kg iv in 10 min, ), partial occlusion of observed vessel with a glass microrod () and a combination of microocclusion and dextran treatment (). Averaged data are given in Table 1. Pattern size is minimal at pseudoshear rates between 100 and 200 s1.

Glass capillaries. Power spectra obtained from recordings in glass capillaries were less homogeneous in shape than those obtained from in vivo experiments. Accordingly, the parameters of the respective fits exhibited a larger degree of scatter. However, the data for the intersection point (Fig. 8) seem to indicate some increase of pattern size with decreasing shear rate and agree approximately with those derived from in vivo recordings for a given level of shear rate.

View larger version (18K): [in this window] [in a new window]   Fig. 8.   Effect of pseudoshear rate on intersection point for spectra obtained in glass tubes with a diameter of 28.5 µm at hematocrits of 20 () and 40 ().

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Power spectra as a tool to investigate flow patterns. The objective of the present study was to develop a tool for the investigation of vascular flow patterns in living microvessels using power spectra of light intensity fluctuations generated by flowing erythrocytes and recorded during intravital microscopy. Compared with a direct analysis of photographic or video images, this approach has a distinctive advantage: The maximal length of continuous traces that can be analyzed is only limited by the sampling period used and can thus be much longer than the average length of microvessel segments, which averages only ~350 µm in the investigated tissue (21). However, because of the irregular distribution of RBCs in microvascular blood flow, the information of prevalent pattern sizes entailed in the light intensity traces is usually not directly apparent in the form of easily recognizable peaks and maxima of the derived power spectra. Therefore, model experiments were performed to develop and validate appropriate interpretation schemes for the spectra obtained from blood flow in microvessels.

A micrometer scale presenting a highly regular, repetitive grid was the only test pattern resulting in a power spectrum with a distinct peak. The location of the peak at a pattern length directly corresponding to the distance of the individual lines of the micrometer scale demonstrates the validity of the optical and analytical setup used (Fig. 2). In contrast, monolayers of Sephadex beads or wet-mount preparations of erythrocytes did not exhibit discernible peaks corresponding to the known size of the beads or the erythrocytes. They showed a decreasing spectral density with increasing spatial frequency or decreasing pattern size. In a double logarithmic representation (Fig. 3), these spectra can be described as two linear parts with different slopes linked by a curved portion in the intermediate frequency range. For beads and RBCs, the intersection of the two straight lines corresponds to a pattern length in close agreement with the average size of the original structural elements: Sephadex beads with an average diameter of 31 µm yielded an intersection point of the straight lines of 33 µm, for RBCs (diameter 7.5 µm) the respective value was 9.6 µm. Thus in both cases the length values obtained from the intersection of the two straight lines are slightly higher than the actual structural diameters of individual particles. This discrepancy relates to the fact that the power spectrum is determined not only by the sizes of the particles themselves but also by the width of the space separating the particles. The numerical length value for the intersection point may therefore be interpreted as an indicator of the typical pattern size, including gaps or as an average center-to-center distance.

This empirical interpretation of the intersection point is supported by a general analysis of the relation between observed spectra and corresponding image characteristics. In the double logarithmic representation, all spectra (with exception of the repetitive regular pattern) exhibited a linear decrease of spectral density with decreasing pattern length at the high frequency end of the spectra. As shown by Mitchell and Bonnell (13) in a topographic analysis of fractal surfaces, a linear negative relationship may indicate self-similarities in the underlying image. Such a self-similar or fractal appearance is also seen in the picture generated by the back transformation of a cone-shaped spectrum (Fig. 4, right column).

For the experimental spectra, the part exhibiting a linear negative slope was restricted to a region corresponding to pattern length values equal or below that of the elementary particle size (Fig. 5). The self-similar or fractal characteristics in this spectral region are likely to be generated by the irregular distribution of particles. A recording line through such a distribution will hit particles both in center and out of center generating a distribution of apparent granulation sizes between zero (tangential) and the elementary pattern diameter (central). The generated spectral power decreases with granulation size. Such a negative spectral slope is most expressed in the experiments with a monolayer of Sephadex beads. A similar characteristic is also seen for spectra of wet-mount RBC preparations and for intravital recordings from microvessels, indicating a fractal probability distribution of apparent granulation sizes in a range below the actual particle size. These small-sized patterns correspond to particles passing the sensor at an eccentric position, to interparticle gaps and, in the case of RBCs, to subcellular heterogeneity of refractive and absorptive characteristics.

The lower frequency end of the spectra, corresponding to high pattern length values, exhibited nearly constant spectral densities in the in vivo recordings of pre- and postcapillary vessels. For completely flat artificial model power spectra, combined with a random phase, reverse transformation (Fig. 4, middle two columns) reveals granulations with a predominant pattern size that directly corresponds to the range-limiting value (radius) of the cylindrical three-dimensional spectrum used. The images generated from such spectra can be compared with those derived from peak-type spectra created by regular repetitive patterns with a fixed pattern size (Fig. 2) or the tube-like three-dimensional spectrum (Fig. 4, left column), where the typical pattern size reflects the position of the peak or the "tube wall." The additional spectral power entailed in the flat portion of the cylindrical spectra only leads to a slight size increase of individual pattern elements in the generated image in comparison to that created by a tube spectrum with the same limiting value. The main difference, however, is a blurring and more irregular arrangement of the contours as well as an increased distance of the pattern elements.

Summing up the analysis of spectra obtained from known test patterns and of images generated by simple model spectra, the following interpretation of experimental spectra is derived. The extrapolated intersection point between the two linear portions (corresponding to the upper-limiting value of the cylindrical model spectra) entails information on the typical size of pattern-creating structures. The extent of the curved transition zone represents the distribution of pattern sizes, and the upper (lower) boundary of this zone corresponds to a maximal (minimal) pattern size. If a negative slope is observed in the spectral region left of the intersection point (e.g., for capillaries), this is indicative of larger irregular (fractal) structures, which add spectral power to the otherwise flat spectrum in this region.

Flow patterns in microvessels. In capillaries with diameters of ~6 µm, the extrapolated intersection between the two linear portions of the spectra always corresponded to a pattern length value of 7.9 µm, close to the diameter of individual RBCs (Figs. 5 and 6). In addition, a curved transition zone corresponding to a distribution of pattern sizes is more or less absent in this diameter range. These data are in line with the results of direct observation showing that capillaries are passed by RBCs under single-file flow conditions (22). The increase of spectral power with decreasing spatial frequency (negative slope of the left straight line) observed in capillaries may correspond to RBC trains (9, 25) constituted by varying numbers of RBCs trapped behind a slow-moving (white) cell and the gaps between them.

The intercept and lower boundary values for pre- and postcapillary vessels range between 7 and 20 µm, depending on vessel diameter and shear rate, indicating that in these vessels the typical patterns are influenced by RBC clusters (Fig. 6). These patterns observed at spontaneous flow conditions (pseudoshear rate above 100 s¹) probably do not represent aggregates in the usual sense of the word, i.e., RBCs linked together by mechanisms such as surface charges and plasma macromolecules. More likely they are short-lived clusters of erythrocytes brought in close contact by hemodynamic forces. This interpretation is supported by the unexpected finding that pattern size increases with increasing shear rate >100 s¹.

In contrast, an increase in pattern size was observed at pseudoshear rates reduced below 100 s¹ in experiments with infusion of high-molecular-weight dextran and local microocclusion (Fig. 7). These changes suggest the generation of additional larger RBC flow patterns due to RBC aggregation at low shear rate levels. High-molecular-weight dextran is known to increase RBC aggregability (10, 27, 29). The concentration used here created a substantial amount of RBC aggregating and clumping in wet-mount preparations of blood drawn from the venous catheter of the treated animals. The present results, however, cannot clearly show that an increased aggregation tendency is a factor independent from shear rate in the generation of microaggregates in the investigated range of pseudoshear rates between 10 and 100 s¹. The formation of RBC flow patterns and especially of microaggregates may have physiological consequences for local oxygen delivery by altering RBC distribution within terminal vascular beds.

In a recently published study, Cabel and co-workers (3) report an inverse relationship between venous vascular resistance and blood flow in cat skeletal muscle, which was abolished if no RBCs were present or aggregation tendency was suppressed. Because the overall venous resistance was enhanced by high-molecular-weight dextran, the observed changes in flow resistance were interpreted to result from changes in RBC aggregation. In the venous part of the terminal vascular bed, shear rates are low and blood flow at branch points is confluent. Thus flow structures are conserved over much longer distances compared with the arterial side, increasing the possible influence of RBC aggregates on flow resistance. In the present study an increase in microaggregate size was seen upon increase of the aggregation tendency with dextran, especially if flow velocity was reduced by mechanical obstruction. However, for the range of vessels studied, there were no indications of significant differences between arteriolar and venular flow patterns in the control situation. This indicates that aggregation tendency of the blood, vessel diameters, and shear rates have to be considered in attempts to understand the impact of RBC aggregation in microvessels on vascular resistance.

In conclusion, the analysis of continuous intensity recordings using Fourier analysis yields quantitative information on typical flow patterns in microvessels in vivo. Because of the short length of typical microvessels and the prevalent RBC velocities, this information cannot directly be obtained by microphotographs or video recordings. The present data show that a principal pattern size nearly identical to that of a single RBC occurs in all in vivo spectra. In typical capillaries, it is the predominant characteristic of the power spectrum. Larger patterns in capillaries may be generated by the typical arrangement of erythrocyte "trains." The situation is different in pre- and postcapillary vessels, where RBCs have sufficient space to form hydrodynamic clusters or microaggregates. Here pattern sizes are minimal at pseudoshear rates of ~150 s¹ and increase both at higher and lower shear rates. The flow structures generated at high shear rates may represent short-lived RBC clusters brought together by hemodynamic forces. At low shear rates elicited in experiments with dextran infusion and local occlusion, the formation of microaggregates probably prevails. The formation (and disruption) of both types of flow structures is likely to contribute to the vascular flow resistance by (entropic) dissipation of energy.