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Regulation of blood flow in individual capillaries of resting skeletal muscle in frogs
MICROVASCULAR RESEARCH 20, 346-357 (1980)
Regulation of Blood Flow in Individual Capillaries of Resting Skeletal Muscle in Frogs KAREL TYML AND ALAN C . GROOM
Department of Biophysics, University of Western Ontario, London, Ontario, N6A 5C1, Canada Received October 26, 1979 We have compared time variations of red cell velocity in two daughter capillaries originating directly from the same metarteriole or terminal arteriole. Our reasoning was that if these variations were similar the regulation of red cell flow must occur primarily at the arteriolar level; if they were dissimilar the regulation must occur separately in each daughter capillary. Velocity was measured by a computerized frame-by-frame analysis of tape-recorded television images of the microcirculation. Measurements in 12 capillary pairs were represented by velocity records with duration and mean velocity ranging from 3. l to 50 min and 0.03 to 0.47 mm/sec, respectively. In each pair, the record from one daughter capillary was filtered with a series of bandpass filters and linearly correlated with the correspondingly filtered record from the other capillary. In the range of periods from 0. I to 78 sec the coefficients of linear correlation were less than 0.36 and therefore the variations were judged to be unrelated. Velocity variations in the range of 5 to 20 min corresponded closely since the overall coefficient was 0.95. It is concluded that, in resting sartorius muscle in anesthetized frogs, arteriolar regulation occurs predominantly on a minute-to-minute basis, and that if any regulation occurs within individual capillaries or the venular part of the network, this must be on a time scale of seconds only. Further, we estimate that the minute-to-minute variations contribute about 18% to the overall variations and the second-to-second uncorrelatable variations as much as 52%.
INTRODUCTION
The site of the regulation of blood flow in individual capillaries in a microvascular network may be thought to exist at two different levels, (1) the arteriolar level at which the regulation could affect the flow in several subsequent capillaries, and (2) the capillary level at which the regulation would be unique to each capillary. There is a large body of experimental evidence for regulation at the arteriolar level. For instance, Johnson and Intaglietta (1976) were able to measure the flow and diameter changes in arterioles of cat mesentery following stepwise reduction in arterial pressure. An example of regulation at the capillary level is that originating from the activity of the precapillary sphincter (defined by Wiedeman et al., 1976). The presence of this type of regulation was reported by Johnson and Wayland (1967) who attributed the periodic flow patterns in capillaries of cat mesentery to the activity of precapillary sphincters. However, this activity is less certain in skeletal muscle; Burton and Johnson (1972) reported that the postocclusion increase of capillary flow in sartorius muscle of cat was more likely mediated at the arteriolar level. In a similar study in pectoralis muscle in frogs, Gentry and 346 0026-2862/80/060346-12502.00/0 Copyright© 1980by AcademicPress, Inc. All rightsof reproductionin any form reserved. Printed in U.S.A.
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Johnson (1972) concluded that capillary flow was regulated solely at the arteriolar level. Eriksson and Lisander (1972) were not able to identify, either morphologically or functionally, the presence of precapillary sphincters in tenuissimus muscle of cat. In our preliminary measurements of the red cell velocity (V rbe) in capillaries of a resting skeletal muscle in frogs, we have noticed that the Vrbc varied with time by at least 100% around its mean value. Therefore it seemed plausible that, by comparing the time variations of Vr~ in two daughter capillaries originating directly from the same terminal arteriole or metarteriole, we could determine what type of regulation occurred in each daughter capillary. Our reasoning was that if these variations were similar then the regulation of blood flow must have occurred primarily at the arteriolar level; if they were dissimilar then regulation must have occurred separately in each daughter capillary. In order to quantify the similarity between the two time variations, we plotted the Vrbc measurements from each daughter capillary against each other, thus eliminating time as a variable. If the two variations were identical, then the coefficient of linear correlation of this plot would be equal to one. On the other hand, if the two variations were completely unrelated, then the coefficient would be equal to zero. METHODS
Animal Preparation Nine frogs (Rana pipiens, 19-39 g in weight) were anesthetized with urethane injected into the dorsal lymph sac (35 mg/10 g of body wt). A sartorius muscle, surrounded by transparent connective tissue, was exposed by removing the overlying skin. The connective tissue at the lateral side of the muscle was dissected so that the lateral edge of the muscle could be gently lifted. A 45° acrylic prism (2.5 mm wide, 2 mm deep, 10 mm long), coupled to a fiber-optic light guide (20 cm long), was inserted underneath the muscle (Fig. 1). Light from a xenon lamp was conducted through the light guide and reflected in the prism to transilluminate the muscle. Possible heating effects of the light transmitted by the guide were investigated by placing a thermocouple between the upper face of the prism and the undersurface of the muscle. The temperatures so recorded with the light on were consistently less than 0.5°C higher than those with the light off. At the upper surface of the muscle the temperature increment would have been substantially mi . . . . . . pe objective /
s a r t o r i u s muscle
~
I
I [
fibre optics
/acrylic prism
FIG. I. Animal preparation. The left-hand side shows the position of the sartorius muscle within the leg of the frog. The right-hand side shows the cross-sectional view of the leg and muscle along the plane indicated by (X X) and the optical arrangement to transilluminate the muscle.
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less than this, since the connective tissue on top of the exposed muscle was kept moist with isotonic NaCI solution (0.114 M) at room temperature (23°). No qualitative differences in the pattern of microvascular flow were observed between the time when the light was first switched on and several minutes later. This confirmed that the effect of the transmitted light on capillary blood flow was negligible. The frog, at room temperature, rested in the supine position on the stage of a microscope (Nikon) and the transilluminated muscle was viewed at a magnification 50×, using a 10× objective (N.A. = 0.25) and a 5× eyepiece. A TV camera (Sony, 2 : I fixed interlace, AVC-3260) was mounted on the microscope to scan the image of the microcirculation in the surface capillaries of the muscle. The magnification of the image of the capillaries was 12.5× at the face of the vidicon tube of the camera and the overall magnification of the image, as seen on the screen of a TV monitor (Electrohome EVM-I 110R), was 360×. The TV camera generated a video signal which was stored on a video tape, thus allowing off-line analysis of different capillaries in the same field of view. The general branching pattern of microvessels in the frog sartorius muscle has been described by Plyley et al. (1976). Figure 2 shows a sketch of a typical pattern in which the terminal arteriole or metarteriole branches into capillaries. We have chosen to measure the red cell velocity in a capillary pair (that is, for instance, in both capillaries C1 and C2) that originated directly from the same terminal arteriole or metarteriole. The diameter of capillaries ranged from 15 to 20/~m and the length appearing on the screen of the TV monitor varied between 160 and 470/zm,
Measurement and Filtering of Red Cell Velocity The Vrbc in capillaries was measured by a television-computer method which operated on the principle that the Vrbc is directly proportional to the displacement of red cells in a fixed time interval (Tyml and Sherebrin, 1980). A video analyzer (Colorado Video Inc., Model 321) samples the video signal and generates an
~*~
terminal arteriole
c4 capillaries
FIG. 2. Patterns of branching of metarteriole and terminal arteriole into capillaries (15 to 20-/zm diameter) in frog sartorius muscle. Red cell velocity was measured in straight portions of each daughter capillary, e.g., $1, S~ in capillaries C1, C2. Lengths of $1 and Sz were equal (160-230/xm) and so were the distances from the branching point (60-100 p,m).
R E G U L A T I O N OF B L O O D F L O W IN C A P I L L A R I E S
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optical density waveform of the content of a capillary. The peaks and valleys of the waveform correspond to the plasma gaps and red cells within the capillary and the shift of the waveform represents the displacement of the cells and gaps. A digital computer system (Cromemco Z-2D) determines the shift by means of the absolute differences between the digitized waveforms; it also calculates velocity points at a fixed rate, R, (max rate is 60/sec), stores them in a computer file, and displays them on a chart recorder. The Vrbc determined by this method is not simply that of a single cell, but rather the mean velocity of a slug of cells and plasma in a capillary segment. In this investigation, the lengths of the straight portions of capillaries selected for red cell velocity measurements ranged from 160 to 230 ~m, but for a given capillary pair the lengths and distances of these portions from the branching point were approximately the same (see S~ and $2 in Fig. 2). The Vr~ in both daughter capillaries was measured by means of videotape playbacks. The audio track of the tape was marked by a cue signal which was used for the synchronization of subsequent playbacks, thus allowing " s i m u l t a n e o u s " Vrb¢ measurements in both capillaries. The two measurements were represented by two velocity records, vl and v2, and stored in two computer files as arrays VH, V~2. . . . . V~v and V21, V22. . . . . V2p. Here P represented the number of velocity points in each file; the total duration, D, of each velocity record was given by D = P/R (sec), where R lay in the range from 4.3 to 10 sec -1 In order to distinguish between the contribution of the fast or slow velocity variations, as far as the similarity or dissimilarity between the two records was concerned, we have filtered the records with a series of low-pass digital filters with different cut-off frequencies. The design of digital filters has been discussed by Hamming (1977). Rather than using a running average (each velocity being weighted equally) we have used a nonrecursive filter in which each point is weighted by a factor Fk, such that Fk = C " Wk " Ak, ak =
sin 2~(kAt)f¢
2~r(kAt)fc)
(1) ,
(2)
Wk = ½(1 + COS 27r(kAt)fc), C -
,
(3) (4)
' W k " Ak k=--m
and k = - m , - m + 1. . . . . - 1, O, 1. . . . . m - 1, m (m being the closest integer to l/2fc~t). H e r e f e represents the cutoff frequency (Hz) of the filter and At the time interval between two successively measured velocity points, At = I/R (sec). Expression (2) describes the filtering function, expression (3) the window function that smoothes out the abrupt changes in the filtering function values at k = _+m (Hamming, 1977) , and expression (4), the normalizing constant. In general, the set of P velocity points V1, V2. . . . . Vp was passed through a low-pass filter
TYML AND GROOM
350
(characterized byfc) to generate a new set in which each point, V~c, was computed as
V~¢ = ~ V,+k " Fk; k=-m
(5)
values o f n were integers ranging from (m + 1) to ( P - m). This set, consisting of (P - 2m) points, represented a record of filtered velocities which, ideally, should contain only a spectrum of periodic components with frequencies less than fc. However, in the filtering procedure described by expression (5), this was not quite true since the filter had a roll-off of 18 db/octave. RESULTS Twenty-four velocity records of different durations were obtained by measuring Vrbc in 12 capillary pairs. The duration of these records ranged from 3.1 to 50 min, their mean Vrbc from 0.03 to 0.47 mm/sec, and their standard deviations from 0.02 to 0.15 mm/sec. An example of such a record is shown in the top panel of Fig. 3. The duration of this record was 50 min (R = 7.5 sec -1, P = 22,500), velocity varied between 0.06 and 0.32 mm/sec, and the mean Vrb~ was 0.13 _ 0.05 SD mm/sec. The middle and bottom panels of this figure show the same record after being passed through low pass filters withf~ = 1/23 and 1/78 Hz, respectively. We have chosen to label all filtered records with the cutoff period, T~, such that T~ = 1~. Figure 4 illustrates the technique with which the similarity between velocity variations in two filtered records was quantified. At the top, vl (redrawn from the bottom of Fig. 3) and v2 represent records obtained from two daughter capillaries; both records contain 21,916 velocity points (i.e., P - 2m, P = 22,500, m = 292). If we plotted all the velocity points of vz against all the corresponding points of vl and also calculated the regression line, then the coefficient of linear correlation would give us a quantitative measure of the similarity between velocity variations in the two records. At the bottom of Fig. 4 only the regression line (calculated by
V4[[mm/sec]
not filtered
.
2
0
~
10
t
20
30
2 0
~ 10
[ml.]
~ 20
Vl
0
50
Tc = 23 sec
vl ,
40
Tc =
10
i
iO
t 30
40
50
[mi-I
7 8 sec
30
i
~10
i
i t
50 [mini
FIG. 3. Velocity record (v0 unfiltered and after filtration through low-pass filters with cutoff periods 23 and 78 sec, respectively.
R E G U L A T I O N OF BLOOD F L O W IN CAPILLARIES
V2[mm/sec] .4] ~
351
To= 78 sec
"V 0 V
i
10
20
1 0
30
" 10
40
2 20
t
SO
t 30
40
50 [ rain]
V2[ mm/secl .4. V2=- 0.014. 1.39VI r =0.97
.3 ~ .2
.1
0
I
.1
' .2
' .3
' V1[mm/sec] .4
FIG. 4. Quantification o f the similarity between velocity records (vl and v~) from two daughter capillaries. If the velocity variations in the two records were identical, then the coefficient of linear correlation, r, would be equal to one. If the variations were completely unrelated, then the coefficient would be equal to zero. All 21,916 points (i.e., P - 2m, P = 22,500, m = 292) from v~ and v2 were used for the correlation, but only the regression line is shown (see text). The slope of the line is equal to the ratio o f mean flows in the two capillaries.
the computer) of such a plot is shown since it was impractical to plot all 21,916 points. In this example the velocity variations between the two records are similar; the coefficient of linear correlation, r, is 0.97 and the slope of the line is equal to the ratio of mean flows in the two capillaries. In the above example, both vl and v2 ideally contain a spectrum of periodic components with periods ranging from 78 sec to at least 50 min. In order to consider a narrower range of periods, as far as its contribution to the similarity or dissimilarity between two records was concerned, the records were further filtered with a series of band-pass filters. Since the filtering procedure described by expression (5) does not introduce any phase lag among filtered velocities from a given record, a band-filtered record can be obtained by calculating the differences between two records filtered at two different Te values. Thus by subtracting the bottom record (Fig. 3) from the middle one a new record is produced that includes only components with periods ranging from 23 to 78 sec. Correlation of this record with the correspondingly filtered record from the other capillary yields information about the similarity between velocity variations in the two daughter capillaries at this particular range of periods. Here r was calculated to be 0.35; values of r in the ranges of T0-3, 3-23, 78-300, and 300-1200 sec are tabulated in Table 1, row A. The lower limit of this overall range of periods, To, was given by the
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TYML AND GROOM TABLE 1
COEFFICIENTS OF LINEAR CORRELATION, r (+ SE), BETWEEN BAND-FILTERED RECORDS OF CELL VELOCITY MEASUREMENTS FROM CAPILLARY PAIRS
Period ranges (sec)
A B C D
T0-3
3-23
23-78
78-300
300-1200
0.30 0.36 __. 0.10 0.91 0.02
0.006 0.02 -+ 0.06 0.96 0.03
0.35 0.20 -+ 0.10 0.98 0.02
0.80 0.63 _+ 0.08 0.99 0.04
0.98 0.95 _+ 0.02 1.00 0.05
Note: A, measurements from one capillary pair; B, combined data from 12 capillary pairs; C, duplicate measurements for a single record; D, two random number sequences. r e c i p r o c a l o f t h e r a t e at w h i c h v e l o c i t y p o i n t s w e r e m e a s u r e d , a n d lay b e t w e e n 0.1 a n d 0.23 s e c . T h e c o m b i n e d d a t a f r o m 12 c a p i l l a r y p a i r s a r e e n t e r e d in r o w B a n d a l s o p l o t t e d in a h i s t o g r a m f o r m in Fig. 5a. DISCUSSION
AND ANALYSIS
The accuracy of the television-computer method for measuring red cell velocity in c a p i l l a r i e s d e p e n d s o n t h e o p t i c a l c o n t r a s t b e t w e e n t h e c e l l s a n d p l a s m a g a p s r ± S.E.
.95 ~ .02
[
a .63±.08
%.36± .10 .20_+.10
TO
3
23
78 period
v(B)/v(u) ±S.E. [Z]
300 ranges
1200 [sec l
70.3± 5.6
@ b 14.1±2.9 10.3 ± 1.9
TO
23
78
300
1200
FIG. 5. Correlation coefficient, r (a), and relative variance, V(B)/V(U) (b), for velocity records filtered (bandpass) for different ranges of periods. V(B) is the variance of a particular filtered record, and V(U) is the variance of the unfiltered record. Values of the lower limit, To, lay in the range 0.10 to 0.23 sec. Relative variances in each range of periods represent the contributions to the overall measured variance. Fifteen percent of this variance is due to uncertainty in the velocity measurement (all in the range To to 3 sec) and 85% represents true biological variation. The total biological variation may be subdivided as follows: second-to-second correlatable variations, due to the heart beat, 30%; second-to-second uncorrelatable variations, 52%; minute-to-minute correlatable variations, 18%.
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(Tyml and Sherebrin, 1980). The better the contrast the larger is the signal-tonoise ratio of the optical density waveform obtained from the video signal. In this study, the noise originated mainly from the videotape playbacks. In order to evaluate how much this electronic noise affected the correlation between different records, we have used two synchronized playbacks to measure the Vrbc in one capillary twice. The two measurements should be identical and so should be their corresponding bandfiltered records. Entries in row C (Table 1) represent the r values for such duplicate records. The departures of these values from unity are measures of the distortion introduced into the correlation process between filtered records. For each range of periods, these departures are significantly smaller than the departures due to biological variations (row A or B) and therefore we claim that the dependence o f r on the different ranges of periods is due to true biological variations of Vrb~. Entries in row D demonstrate that for unrelated variations r values are bound to be near zero. In this example, velocity measurements from two daughter capillaries were simulated by two random number sequences. In each sequence, the range of the simulated velocities was similar to that of a true velocity record; the mean was 0.13 mm/sec, R = 7.5 sec-', and P = 17,720. In our earlier analysis of velocity measurements in capillaries of resting skeletal muscle in frogs (Tyml and Groom, 1980) we have determined that the velocity variations consisted of irregular fluctuations with a superimposed pulsatile component caused by the pumping action of the heart. Referring to Fig. 5a it is apparent that the variations including periodic components in the range of 300 to 1200 sec correlated very well (r -- 0.95 _+ 0.02 SE). This high correlation implies that 90% (-- r 2) of the variation in the one capillary was linearly related to that in the second capillary, and that in this range of periods the velocity fluctuations in both daughter capillaries were similar. In the range of periods from 78 to 300 sec the overall r value for the 12 capillary pairs was 0.63 _ 0.08 SE. The values varied between 0.14 and 0.98 indicating that within this band of periods there were capillary pairs with three types of velocity fluctuations. The first type included the correlatable fluctuations with high r values, the second type the uncorrelatable ones with low r values, and the third type a mixture of both. Velocity fluctuations in the range of periods from 23 to 78 sec are those of the second type since, on the average, only 4% of the variation in one capillary was linearly related to that in the second one. In the band of periods from 3 to 23 sec the velocity fluctuations in both daughter capillaries were completely unrelated since the r value was not statistically different from zero. The range from the lowest detectable period To up to 3 sec includes the correlatable puisatile component due to the heart beat, and therefore its average r value is larger than that of the neighboring band. Since only 12% of the variation in the one capillary was linearly related to that in the second capillary we claim that, in this band, the nonpulsatile fluctuations were also unrelated. The question arises: what was the contribution of the velocity variation in one particular band to the overall velocity variation? We have calculated the variances of the unfiltered records, V(U), and the variances of all the band-filtered records, V(B). For each record the sum of the V(B)'s was practically equal to V(U) and therefore the contribution from each band could be expressed as the ratio of the particular V(B) to V(U). Figure 5b shows the ratios (expressed in percentage)
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TYML A N D GROOM
combined from all velocity records. The largest contribution (70.3% ___5.6 SE) to the overall velocity variation occurred in the range from To to 3 sec. Using the overall variance of the unfiltered records and the overall amplitude of the pulsatile component (previously measured as 54.3 ~m/sec with a period of 1.5 sec at room temperature) we have estimated that the pulsatility due to the heart beat contributed about 25% of the total variation. Error in the velocity measurement will contribute a variation of 10-15% and, therefore, we have concluded that in this lowest band of periods the uncorrelatable Vrbc variation amounted to at least 30% of the overall variation. Contributions of the uncorrelatable variations (bands of 3-23 and 23-78 sec), mixed variations (78-300 sec), and correlatable variations (300-1200 sec or 5-20 min) were 10.3, 2.2, 1.9, and 14.1%, respectively. The analysis presented in the previous paragraphs suggests that in each capillary pair the velocity variations consisted of components that could be separated, on the basis of their periods, into two groups. The first group represented the uncorrelatable variations (including components with periods ranging from To to roughly 1 or 2 min and the second group represented the correlatable variations (with periods ranging roughly from 1 or 2 to 20 minutes). We chose to call the variations in the first group the "second-to-second" variations (they predominated in the range from To to 23 sec) and those in the second group the "minuteto-minute" variations. How can one interpret the results shown in Figs. 5a and b? The high correlation in the range from 300 to 1200 sec indicates that the minute-to-minute regulation of blood flow occurs at the arteriolar level. However, there exists a possibility that this regulation may also occur at the level of each daughter capillary. This possibility assumes that the regulation is mediated, for example, via humoral or metabolic agents released into the same microenvironment of both capillaries and thus causing simultaneous flow adjustments in both vessels. In order to examine this possibility, we have compared visually, from the television screen, red cell velocity variations in one daughter capillary with the corresponding velocity variations in another capillary that was situated in the same microenvironment but originated from a different arteriole. If the velocity variations in these two capillaries were similar, then the possibility that parallel capillaries situated in the same microenvironment were reacting simultaneously to a regulatory agent could not be excluded. On the other hand, if the variations were unrelated, then the regulation must have occurred at the arteriolar level. Since no similarity between these two variations was found, we interpret the high correlation between variations in two daughter capillaries as regulation of blood flow via the parent arteriole on a minute-to-minute basis. The absence of correlation in the band of T0-3 sec could be due to theological factors affecting the red cell flow in each capillary. These fast fluctuations are unlikely to represent the regulation of blood flow as such, for this would tend to damp out the pulsatility of flow associated with the heart beat; it may be that they merely reflect the momentary changes in the resistance to flow in capillaries caused by the red cells themselves. From our video recordings of microvascular flow we have observed that red cells (a) enter the capillary either as individual cells or in slugs of different sizes, (b) reorient themselves during their passage through the capillary, and (c) may occasionally even stick to the capillary wall.
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In order to estimate the range of periods of the rheological noise caused by red cells passing through a capillary, cases (a) and (b) above, we have used values of both the mean capillary length and the mean velocity to calculate the average residence time of each cell in a capillary. Plyley et al. (1976) reported that the mean length of the capillary segment (i.e., the length of a capillary between two branching points) in the frog sartorius muscle was 0.85 mm. In our study, the overall mean velocity in capillary segments of the same muscle was 0.20 mm/sec. Since each red cell or slug of cells resided, on the average, not more than 4.25 sec (= 0.85/0.20) within a particular capillary segment, we estimate that this rheological noise does not include periods much greater than 4.25 sec. Occasionally, we have also observed red cells sticking to the capillary wall. During their contact with the wall, these cells caused an increased resistance to flow by partially obstructing the capillary lumen. In order to appreciate the contribution of this phenomenon to the overall rheological noise, we have measured both the incidence of cell sticking and the duration of the cell-wall contact in all 24 capillaries subjected to the velocity analysis described earlier. During 373 min of red cell flow the cells stopped 38 times for an average time interval of 1.65 sec (see Fig. 6). The longest interval was 4.5 sec. Referring to the analysis presented in the previous two paragraphs, one could explain the absence of correlation in the bands of T0-3 and 3-23 sec in terms of the rheological noise that is unique for each daughter capillary. But what about the slower uncorrelatable velocity variations in the band of 23-78 sec and, in some capillary pairs, in the band of 78-300 sec? Absence of correlation in these bands must also be caused by a process altering the red cell velocity separately in each daughter capillary. We believe, however, that this process cannot be theological noise, as discussed above, since that would introduce flow fluctuations that are much too fast to account for the slower variations which these bands represent. What then is this process'? We suspect that these slower variations are caused by changes in the resistance to flow mediated via changes in the luminal diameters of microvessels situated downstream from the branching point of the two capillaries. Referring to Fig. 5b, the slower variations represent only a few percent of the overall variations and therefore one would expect the changes in the luminal diameter to be also very small. In our video recordings of microvascular flow the number of
17
counts
11
0
2 duration
3
4
of c e l l - w a l l c o n t a c t
5
Is.el
FIG. 6. Histogram of the duration of the cell-wall contact. During the total of 373 min of red cell flow in 24 capillaries the red cells stuck to the capillary lumen 38 times for an average time interval of 1.65 sec.
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T Y M L A N D GROOM
quality of the television picture was not good enough to measure such small changes; however, on several occasions, we were able to observe a region along a capillary where the lumen appeared to be narrower than that in the adjacent region. This "bottleneck" was situated either at the capillary entrance or several hundred micrometers away from it; its diameter was roughly 70% of the capillary diameter and its length was about one or two capillary diameters. Existence of similar "bottleneck" regions was reported by L~ibbers et al. (1979). They found that on electrical stimulation of capillaries in the rabbit mesentery blood flow was reduced, in 43 out of 63 capillaries, by a bulging of the nucleus of "special" endothelial cells in to the capillary lumen. Similar bulging was also found in endothelial cells of capillaries in the frog mesentery. These authors suggested that the bulging of specialized endothelial cells could mediate the regulation of capillary blood flow. Is it possible, then, that the slower velocity variations found in the present study were caused by the above mechanism? We do not know, but there certainly is evidence that endothelial cells in some tissues are capable of contraction. Ludatscher (1978) examined the ultrastructure of endothelial cells in venous capillaries and venules in human skin and found that some of these cells included an abundance of contractile filaments and showed, occasionally, bulging endothelial nuclei. The slower variations could also be caused by changes in the resistance to flow mediated via precapillary sphincters, or via changes in luminal diameter as described by Hauck et al. (1977). So far there has been no morphological evidence to show that sphincters exist in skeletal muscle; since we were not able to observe, in this preparation, any movement of the lumen at the capillary entrance, we suspect either that sphincters did not exist or that their activity was minimal. We also have not observed any of the funnel-shaped narrowings of the capillary lumen as reported by Hauck et al. (1977). These narrowings, 300 to 500 p,m away from the capillary branching, were seen in electrically stimulated capillaries in the rabbit mesentery. Assuming that the uncorrelatable velocity variations in the band of 23-78 sec, and possibly also in bands of 3-23 and 78-300 sec, provide indirect evidence for regulation of blood flow at the capillary level, the question arises: where does this regulation occur? One possibility is that the regulation takes place within each daughter capillary; the second possibility is that the regulation occurs in subsequent parts of the microvascular network such as venous capillaries or venules. In order to explain the absence of correlation between velocity variations in the two daughter capillaries, this second possibility must assume drainage of each daughter capillary into different venous capillaries or venules. If any resistance changes occurred in the venular part of the network, then the effect would most likely be uncorrelatable pressure changes at the outflow of each daughter capillary. Since the pressure at the inflow is the same for both capillaries, these uncorrelatable pressure changes would also result in uncorrelatable velocity fluctuations. In one experiment we were able to measure Vr~ in a rather special capillary pair: one of the capillaries rejoined the other after 300 p~m, thus forming a loop with identical inflow and outflow pressures for both microvessels. The values o f t for the different bands of periods, in this instance, were similar to those of Fig.
REGULATION OF BLOOD F L O W IN CAPILLARIES
357
5a and therefore we considered this as evidence for the first possibility, i.e., a separate regulatory process within each capillary. We conclude that in resting sartorius muscle in anesthetized frogs the arteriolar regulation of Vrbc Occurs predominantly on a minute-to-minute basis, and if any regulation occurs within individual capillaries or in subsequent parts of the microvascular network, this must be on a time scale of seconds only. Further, we estimate (Fig. 5b) that the minute-to-minute variations contribute about 18% to the overall biological variations and the second-to-second uncorrelatable variations as much as 52%. ACKNOWLEDGMENTS A part of the material in this paper was presented at the Second World Congress for Microcirculation, La Jolla, California, July 1979. This work was supported by the Studentship of the Medical Research Council awarded to K. Tyml and by a grant from the Ontario Heart Foundation awarded to A. C. Groom. The authors wish to express their great appreciation to Dr. C. Ellis for his helpful comments and stimulating discussions.
REFERENCES BURTON, K. S., AND JOHNSON, P. C. (1972). Reactive hyperemia in individual capillaries of skeletal muscle. Amer. J. Physiol. 223, 517-524. ERIKSSON, E., AND LlSANDER, B. (1972). Changes in precapillary resistance in skeletal muscle vessels studied by intravital microscopy. Acta Physiol. Scand. 84, 295-305. GENTRY, R. M., AND JOHNSON, P. C. (1972). Reactive hyperemia in arterioles and capillaries of frog skeletal muscle following microocclusion. Circ. Res. 31, 953-965. HAMMING, R. W. (1977). "Digital Filters," Prentice-Hall, Englewood Cliffs, N.J. HAUCK, G., WEIOELT, H., AND L~BaERS, D. W. (1977). Is there a possibility to influence blood flow in the capillary network of the mesentery of the rabbit by means of electrical stimulation? Bibl. Anat. 15(1), 448-451. JOHNSON, P. C., AND |NTAGLIETTA, M. (1976). Contributions of pressure and flow sensitivity to autoregulation in mesenteric arterioles. Amer. J. Physiol. 231(6), 1686-1698. JOHNSON, P. C., AND WAYLAND, H. (1967). Regulation of blood flow in single capillaries. Amer. J. Physiol. 212(6), 1405-1415. LI3BBERS, D. W., HAUCK, G., WEIGELT, H., AND ADDICKS, K. (1979). Contractile properties of frog capillaries tested by electrical stimulation. Bibl. Anat. 17, 3-10. LUDATSCHER, R. (1978). Ultrastructure of human dermal blood vessels with special reference to the endothelial filaments. Virchows Arch. B 27, 347-357. PLVLEY, M. J., SUTrlERLAND, G. J., AND GROOM, A. C. (1976). Geometry of the capillary network in skeletal muscle. Microvasc. Res. 11, 161-173. TYML, K., AND GROOM, A. C. (1980). Fourier transform analysis of periodic variations of red cell velocity in capillaries of resting skeletal muscle in frogs. Microvasc. Res. 20, 9-18. TVNL, K., AND SHEREHRIN, M. H. (1980). A method for on-line measurements of red cell velocity in microvessels using computerized frame-by-frame analysis of television images. Microvasc. Res. 20, 1-8. WIEDEMAN, M. P., TUMA, R. F., AND MAYROWITZ, H. N. (1976). Defining the precapillary sphincter. Microvasc. Res. 12, 71-75.
Regulation of Blood Flow in Individual Capillaries of Resting Skeletal Muscle in Frogs KAREL TYML AND ALAN C . GROOM
Department of Biophysics, University of Western Ontario, London, Ontario, N6A 5C1, Canada Received October 26, 1979 We have compared time variations of red cell velocity in two daughter capillaries originating directly from the same metarteriole or terminal arteriole. Our reasoning was that if these variations were similar the regulation of red cell flow must occur primarily at the arteriolar level; if they were dissimilar the regulation must occur separately in each daughter capillary. Velocity was measured by a computerized frame-by-frame analysis of tape-recorded television images of the microcirculation. Measurements in 12 capillary pairs were represented by velocity records with duration and mean velocity ranging from 3. l to 50 min and 0.03 to 0.47 mm/sec, respectively. In each pair, the record from one daughter capillary was filtered with a series of bandpass filters and linearly correlated with the correspondingly filtered record from the other capillary. In the range of periods from 0. I to 78 sec the coefficients of linear correlation were less than 0.36 and therefore the variations were judged to be unrelated. Velocity variations in the range of 5 to 20 min corresponded closely since the overall coefficient was 0.95. It is concluded that, in resting sartorius muscle in anesthetized frogs, arteriolar regulation occurs predominantly on a minute-to-minute basis, and that if any regulation occurs within individual capillaries or the venular part of the network, this must be on a time scale of seconds only. Further, we estimate that the minute-to-minute variations contribute about 18% to the overall variations and the second-to-second uncorrelatable variations as much as 52%.
INTRODUCTION
The site of the regulation of blood flow in individual capillaries in a microvascular network may be thought to exist at two different levels, (1) the arteriolar level at which the regulation could affect the flow in several subsequent capillaries, and (2) the capillary level at which the regulation would be unique to each capillary. There is a large body of experimental evidence for regulation at the arteriolar level. For instance, Johnson and Intaglietta (1976) were able to measure the flow and diameter changes in arterioles of cat mesentery following stepwise reduction in arterial pressure. An example of regulation at the capillary level is that originating from the activity of the precapillary sphincter (defined by Wiedeman et al., 1976). The presence of this type of regulation was reported by Johnson and Wayland (1967) who attributed the periodic flow patterns in capillaries of cat mesentery to the activity of precapillary sphincters. However, this activity is less certain in skeletal muscle; Burton and Johnson (1972) reported that the postocclusion increase of capillary flow in sartorius muscle of cat was more likely mediated at the arteriolar level. In a similar study in pectoralis muscle in frogs, Gentry and 346 0026-2862/80/060346-12502.00/0 Copyright© 1980by AcademicPress, Inc. All rightsof reproductionin any form reserved. Printed in U.S.A.
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Johnson (1972) concluded that capillary flow was regulated solely at the arteriolar level. Eriksson and Lisander (1972) were not able to identify, either morphologically or functionally, the presence of precapillary sphincters in tenuissimus muscle of cat. In our preliminary measurements of the red cell velocity (V rbe) in capillaries of a resting skeletal muscle in frogs, we have noticed that the Vrbc varied with time by at least 100% around its mean value. Therefore it seemed plausible that, by comparing the time variations of Vr~ in two daughter capillaries originating directly from the same terminal arteriole or metarteriole, we could determine what type of regulation occurred in each daughter capillary. Our reasoning was that if these variations were similar then the regulation of blood flow must have occurred primarily at the arteriolar level; if they were dissimilar then regulation must have occurred separately in each daughter capillary. In order to quantify the similarity between the two time variations, we plotted the Vrbc measurements from each daughter capillary against each other, thus eliminating time as a variable. If the two variations were identical, then the coefficient of linear correlation of this plot would be equal to one. On the other hand, if the two variations were completely unrelated, then the coefficient would be equal to zero. METHODS
Animal Preparation Nine frogs (Rana pipiens, 19-39 g in weight) were anesthetized with urethane injected into the dorsal lymph sac (35 mg/10 g of body wt). A sartorius muscle, surrounded by transparent connective tissue, was exposed by removing the overlying skin. The connective tissue at the lateral side of the muscle was dissected so that the lateral edge of the muscle could be gently lifted. A 45° acrylic prism (2.5 mm wide, 2 mm deep, 10 mm long), coupled to a fiber-optic light guide (20 cm long), was inserted underneath the muscle (Fig. 1). Light from a xenon lamp was conducted through the light guide and reflected in the prism to transilluminate the muscle. Possible heating effects of the light transmitted by the guide were investigated by placing a thermocouple between the upper face of the prism and the undersurface of the muscle. The temperatures so recorded with the light on were consistently less than 0.5°C higher than those with the light off. At the upper surface of the muscle the temperature increment would have been substantially mi . . . . . . pe objective /
s a r t o r i u s muscle
~
I
I [
fibre optics
/acrylic prism
FIG. I. Animal preparation. The left-hand side shows the position of the sartorius muscle within the leg of the frog. The right-hand side shows the cross-sectional view of the leg and muscle along the plane indicated by (X X) and the optical arrangement to transilluminate the muscle.
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TYML AND GROOM
less than this, since the connective tissue on top of the exposed muscle was kept moist with isotonic NaCI solution (0.114 M) at room temperature (23°). No qualitative differences in the pattern of microvascular flow were observed between the time when the light was first switched on and several minutes later. This confirmed that the effect of the transmitted light on capillary blood flow was negligible. The frog, at room temperature, rested in the supine position on the stage of a microscope (Nikon) and the transilluminated muscle was viewed at a magnification 50×, using a 10× objective (N.A. = 0.25) and a 5× eyepiece. A TV camera (Sony, 2 : I fixed interlace, AVC-3260) was mounted on the microscope to scan the image of the microcirculation in the surface capillaries of the muscle. The magnification of the image of the capillaries was 12.5× at the face of the vidicon tube of the camera and the overall magnification of the image, as seen on the screen of a TV monitor (Electrohome EVM-I 110R), was 360×. The TV camera generated a video signal which was stored on a video tape, thus allowing off-line analysis of different capillaries in the same field of view. The general branching pattern of microvessels in the frog sartorius muscle has been described by Plyley et al. (1976). Figure 2 shows a sketch of a typical pattern in which the terminal arteriole or metarteriole branches into capillaries. We have chosen to measure the red cell velocity in a capillary pair (that is, for instance, in both capillaries C1 and C2) that originated directly from the same terminal arteriole or metarteriole. The diameter of capillaries ranged from 15 to 20/~m and the length appearing on the screen of the TV monitor varied between 160 and 470/zm,
Measurement and Filtering of Red Cell Velocity The Vrbc in capillaries was measured by a television-computer method which operated on the principle that the Vrbc is directly proportional to the displacement of red cells in a fixed time interval (Tyml and Sherebrin, 1980). A video analyzer (Colorado Video Inc., Model 321) samples the video signal and generates an
~*~
terminal arteriole
c4 capillaries
FIG. 2. Patterns of branching of metarteriole and terminal arteriole into capillaries (15 to 20-/zm diameter) in frog sartorius muscle. Red cell velocity was measured in straight portions of each daughter capillary, e.g., $1, S~ in capillaries C1, C2. Lengths of $1 and Sz were equal (160-230/xm) and so were the distances from the branching point (60-100 p,m).
R E G U L A T I O N OF B L O O D F L O W IN C A P I L L A R I E S
349
optical density waveform of the content of a capillary. The peaks and valleys of the waveform correspond to the plasma gaps and red cells within the capillary and the shift of the waveform represents the displacement of the cells and gaps. A digital computer system (Cromemco Z-2D) determines the shift by means of the absolute differences between the digitized waveforms; it also calculates velocity points at a fixed rate, R, (max rate is 60/sec), stores them in a computer file, and displays them on a chart recorder. The Vrbc determined by this method is not simply that of a single cell, but rather the mean velocity of a slug of cells and plasma in a capillary segment. In this investigation, the lengths of the straight portions of capillaries selected for red cell velocity measurements ranged from 160 to 230 ~m, but for a given capillary pair the lengths and distances of these portions from the branching point were approximately the same (see S~ and $2 in Fig. 2). The Vr~ in both daughter capillaries was measured by means of videotape playbacks. The audio track of the tape was marked by a cue signal which was used for the synchronization of subsequent playbacks, thus allowing " s i m u l t a n e o u s " Vrb¢ measurements in both capillaries. The two measurements were represented by two velocity records, vl and v2, and stored in two computer files as arrays VH, V~2. . . . . V~v and V21, V22. . . . . V2p. Here P represented the number of velocity points in each file; the total duration, D, of each velocity record was given by D = P/R (sec), where R lay in the range from 4.3 to 10 sec -1 In order to distinguish between the contribution of the fast or slow velocity variations, as far as the similarity or dissimilarity between the two records was concerned, we have filtered the records with a series of low-pass digital filters with different cut-off frequencies. The design of digital filters has been discussed by Hamming (1977). Rather than using a running average (each velocity being weighted equally) we have used a nonrecursive filter in which each point is weighted by a factor Fk, such that Fk = C " Wk " Ak, ak =
sin 2~(kAt)f¢
2~r(kAt)fc)
(1) ,
(2)
Wk = ½(1 + COS 27r(kAt)fc), C -
,
(3) (4)
' W k " Ak k=--m
and k = - m , - m + 1. . . . . - 1, O, 1. . . . . m - 1, m (m being the closest integer to l/2fc~t). H e r e f e represents the cutoff frequency (Hz) of the filter and At the time interval between two successively measured velocity points, At = I/R (sec). Expression (2) describes the filtering function, expression (3) the window function that smoothes out the abrupt changes in the filtering function values at k = _+m (Hamming, 1977) , and expression (4), the normalizing constant. In general, the set of P velocity points V1, V2. . . . . Vp was passed through a low-pass filter
TYML AND GROOM
350
(characterized byfc) to generate a new set in which each point, V~c, was computed as
V~¢ = ~ V,+k " Fk; k=-m
(5)
values o f n were integers ranging from (m + 1) to ( P - m). This set, consisting of (P - 2m) points, represented a record of filtered velocities which, ideally, should contain only a spectrum of periodic components with frequencies less than fc. However, in the filtering procedure described by expression (5), this was not quite true since the filter had a roll-off of 18 db/octave. RESULTS Twenty-four velocity records of different durations were obtained by measuring Vrbc in 12 capillary pairs. The duration of these records ranged from 3.1 to 50 min, their mean Vrbc from 0.03 to 0.47 mm/sec, and their standard deviations from 0.02 to 0.15 mm/sec. An example of such a record is shown in the top panel of Fig. 3. The duration of this record was 50 min (R = 7.5 sec -1, P = 22,500), velocity varied between 0.06 and 0.32 mm/sec, and the mean Vrb~ was 0.13 _ 0.05 SD mm/sec. The middle and bottom panels of this figure show the same record after being passed through low pass filters withf~ = 1/23 and 1/78 Hz, respectively. We have chosen to label all filtered records with the cutoff period, T~, such that T~ = 1~. Figure 4 illustrates the technique with which the similarity between velocity variations in two filtered records was quantified. At the top, vl (redrawn from the bottom of Fig. 3) and v2 represent records obtained from two daughter capillaries; both records contain 21,916 velocity points (i.e., P - 2m, P = 22,500, m = 292). If we plotted all the velocity points of vz against all the corresponding points of vl and also calculated the regression line, then the coefficient of linear correlation would give us a quantitative measure of the similarity between velocity variations in the two records. At the bottom of Fig. 4 only the regression line (calculated by
V4[[mm/sec]
not filtered
.
2
0
~
10
t
20
30
2 0
~ 10
[ml.]
~ 20
Vl
0
50
Tc = 23 sec
vl ,
40
Tc =
10
i
iO
t 30
40
50
[mi-I
7 8 sec
30
i
~10
i
i t
50 [mini
FIG. 3. Velocity record (v0 unfiltered and after filtration through low-pass filters with cutoff periods 23 and 78 sec, respectively.
R E G U L A T I O N OF BLOOD F L O W IN CAPILLARIES
V2[mm/sec] .4] ~
351
To= 78 sec
"V 0 V
i
10
20
1 0
30
" 10
40
2 20
t
SO
t 30
40
50 [ rain]
V2[ mm/secl .4. V2=- 0.014. 1.39VI r =0.97
.3 ~ .2
.1
0
I
.1
' .2
' .3
' V1[mm/sec] .4
FIG. 4. Quantification o f the similarity between velocity records (vl and v~) from two daughter capillaries. If the velocity variations in the two records were identical, then the coefficient of linear correlation, r, would be equal to one. If the variations were completely unrelated, then the coefficient would be equal to zero. All 21,916 points (i.e., P - 2m, P = 22,500, m = 292) from v~ and v2 were used for the correlation, but only the regression line is shown (see text). The slope of the line is equal to the ratio o f mean flows in the two capillaries.
the computer) of such a plot is shown since it was impractical to plot all 21,916 points. In this example the velocity variations between the two records are similar; the coefficient of linear correlation, r, is 0.97 and the slope of the line is equal to the ratio of mean flows in the two capillaries. In the above example, both vl and v2 ideally contain a spectrum of periodic components with periods ranging from 78 sec to at least 50 min. In order to consider a narrower range of periods, as far as its contribution to the similarity or dissimilarity between two records was concerned, the records were further filtered with a series of band-pass filters. Since the filtering procedure described by expression (5) does not introduce any phase lag among filtered velocities from a given record, a band-filtered record can be obtained by calculating the differences between two records filtered at two different Te values. Thus by subtracting the bottom record (Fig. 3) from the middle one a new record is produced that includes only components with periods ranging from 23 to 78 sec. Correlation of this record with the correspondingly filtered record from the other capillary yields information about the similarity between velocity variations in the two daughter capillaries at this particular range of periods. Here r was calculated to be 0.35; values of r in the ranges of T0-3, 3-23, 78-300, and 300-1200 sec are tabulated in Table 1, row A. The lower limit of this overall range of periods, To, was given by the
352
TYML AND GROOM TABLE 1
COEFFICIENTS OF LINEAR CORRELATION, r (+ SE), BETWEEN BAND-FILTERED RECORDS OF CELL VELOCITY MEASUREMENTS FROM CAPILLARY PAIRS
Period ranges (sec)
A B C D
T0-3
3-23
23-78
78-300
300-1200
0.30 0.36 __. 0.10 0.91 0.02
0.006 0.02 -+ 0.06 0.96 0.03
0.35 0.20 -+ 0.10 0.98 0.02
0.80 0.63 _+ 0.08 0.99 0.04
0.98 0.95 _+ 0.02 1.00 0.05
Note: A, measurements from one capillary pair; B, combined data from 12 capillary pairs; C, duplicate measurements for a single record; D, two random number sequences. r e c i p r o c a l o f t h e r a t e at w h i c h v e l o c i t y p o i n t s w e r e m e a s u r e d , a n d lay b e t w e e n 0.1 a n d 0.23 s e c . T h e c o m b i n e d d a t a f r o m 12 c a p i l l a r y p a i r s a r e e n t e r e d in r o w B a n d a l s o p l o t t e d in a h i s t o g r a m f o r m in Fig. 5a. DISCUSSION
AND ANALYSIS
The accuracy of the television-computer method for measuring red cell velocity in c a p i l l a r i e s d e p e n d s o n t h e o p t i c a l c o n t r a s t b e t w e e n t h e c e l l s a n d p l a s m a g a p s r ± S.E.
.95 ~ .02
[
a .63±.08
%.36± .10 .20_+.10
TO
3
23
78 period
v(B)/v(u) ±S.E. [Z]
300 ranges
1200 [sec l
70.3± 5.6
@ b 14.1±2.9 10.3 ± 1.9
TO
23
78
300
1200
FIG. 5. Correlation coefficient, r (a), and relative variance, V(B)/V(U) (b), for velocity records filtered (bandpass) for different ranges of periods. V(B) is the variance of a particular filtered record, and V(U) is the variance of the unfiltered record. Values of the lower limit, To, lay in the range 0.10 to 0.23 sec. Relative variances in each range of periods represent the contributions to the overall measured variance. Fifteen percent of this variance is due to uncertainty in the velocity measurement (all in the range To to 3 sec) and 85% represents true biological variation. The total biological variation may be subdivided as follows: second-to-second correlatable variations, due to the heart beat, 30%; second-to-second uncorrelatable variations, 52%; minute-to-minute correlatable variations, 18%.
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353
(Tyml and Sherebrin, 1980). The better the contrast the larger is the signal-tonoise ratio of the optical density waveform obtained from the video signal. In this study, the noise originated mainly from the videotape playbacks. In order to evaluate how much this electronic noise affected the correlation between different records, we have used two synchronized playbacks to measure the Vrbc in one capillary twice. The two measurements should be identical and so should be their corresponding bandfiltered records. Entries in row C (Table 1) represent the r values for such duplicate records. The departures of these values from unity are measures of the distortion introduced into the correlation process between filtered records. For each range of periods, these departures are significantly smaller than the departures due to biological variations (row A or B) and therefore we claim that the dependence o f r on the different ranges of periods is due to true biological variations of Vrb~. Entries in row D demonstrate that for unrelated variations r values are bound to be near zero. In this example, velocity measurements from two daughter capillaries were simulated by two random number sequences. In each sequence, the range of the simulated velocities was similar to that of a true velocity record; the mean was 0.13 mm/sec, R = 7.5 sec-', and P = 17,720. In our earlier analysis of velocity measurements in capillaries of resting skeletal muscle in frogs (Tyml and Groom, 1980) we have determined that the velocity variations consisted of irregular fluctuations with a superimposed pulsatile component caused by the pumping action of the heart. Referring to Fig. 5a it is apparent that the variations including periodic components in the range of 300 to 1200 sec correlated very well (r -- 0.95 _+ 0.02 SE). This high correlation implies that 90% (-- r 2) of the variation in the one capillary was linearly related to that in the second capillary, and that in this range of periods the velocity fluctuations in both daughter capillaries were similar. In the range of periods from 78 to 300 sec the overall r value for the 12 capillary pairs was 0.63 _ 0.08 SE. The values varied between 0.14 and 0.98 indicating that within this band of periods there were capillary pairs with three types of velocity fluctuations. The first type included the correlatable fluctuations with high r values, the second type the uncorrelatable ones with low r values, and the third type a mixture of both. Velocity fluctuations in the range of periods from 23 to 78 sec are those of the second type since, on the average, only 4% of the variation in one capillary was linearly related to that in the second one. In the band of periods from 3 to 23 sec the velocity fluctuations in both daughter capillaries were completely unrelated since the r value was not statistically different from zero. The range from the lowest detectable period To up to 3 sec includes the correlatable puisatile component due to the heart beat, and therefore its average r value is larger than that of the neighboring band. Since only 12% of the variation in the one capillary was linearly related to that in the second capillary we claim that, in this band, the nonpulsatile fluctuations were also unrelated. The question arises: what was the contribution of the velocity variation in one particular band to the overall velocity variation? We have calculated the variances of the unfiltered records, V(U), and the variances of all the band-filtered records, V(B). For each record the sum of the V(B)'s was practically equal to V(U) and therefore the contribution from each band could be expressed as the ratio of the particular V(B) to V(U). Figure 5b shows the ratios (expressed in percentage)
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TYML A N D GROOM
combined from all velocity records. The largest contribution (70.3% ___5.6 SE) to the overall velocity variation occurred in the range from To to 3 sec. Using the overall variance of the unfiltered records and the overall amplitude of the pulsatile component (previously measured as 54.3 ~m/sec with a period of 1.5 sec at room temperature) we have estimated that the pulsatility due to the heart beat contributed about 25% of the total variation. Error in the velocity measurement will contribute a variation of 10-15% and, therefore, we have concluded that in this lowest band of periods the uncorrelatable Vrbc variation amounted to at least 30% of the overall variation. Contributions of the uncorrelatable variations (bands of 3-23 and 23-78 sec), mixed variations (78-300 sec), and correlatable variations (300-1200 sec or 5-20 min) were 10.3, 2.2, 1.9, and 14.1%, respectively. The analysis presented in the previous paragraphs suggests that in each capillary pair the velocity variations consisted of components that could be separated, on the basis of their periods, into two groups. The first group represented the uncorrelatable variations (including components with periods ranging from To to roughly 1 or 2 min and the second group represented the correlatable variations (with periods ranging roughly from 1 or 2 to 20 minutes). We chose to call the variations in the first group the "second-to-second" variations (they predominated in the range from To to 23 sec) and those in the second group the "minuteto-minute" variations. How can one interpret the results shown in Figs. 5a and b? The high correlation in the range from 300 to 1200 sec indicates that the minute-to-minute regulation of blood flow occurs at the arteriolar level. However, there exists a possibility that this regulation may also occur at the level of each daughter capillary. This possibility assumes that the regulation is mediated, for example, via humoral or metabolic agents released into the same microenvironment of both capillaries and thus causing simultaneous flow adjustments in both vessels. In order to examine this possibility, we have compared visually, from the television screen, red cell velocity variations in one daughter capillary with the corresponding velocity variations in another capillary that was situated in the same microenvironment but originated from a different arteriole. If the velocity variations in these two capillaries were similar, then the possibility that parallel capillaries situated in the same microenvironment were reacting simultaneously to a regulatory agent could not be excluded. On the other hand, if the variations were unrelated, then the regulation must have occurred at the arteriolar level. Since no similarity between these two variations was found, we interpret the high correlation between variations in two daughter capillaries as regulation of blood flow via the parent arteriole on a minute-to-minute basis. The absence of correlation in the band of T0-3 sec could be due to theological factors affecting the red cell flow in each capillary. These fast fluctuations are unlikely to represent the regulation of blood flow as such, for this would tend to damp out the pulsatility of flow associated with the heart beat; it may be that they merely reflect the momentary changes in the resistance to flow in capillaries caused by the red cells themselves. From our video recordings of microvascular flow we have observed that red cells (a) enter the capillary either as individual cells or in slugs of different sizes, (b) reorient themselves during their passage through the capillary, and (c) may occasionally even stick to the capillary wall.
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355
In order to estimate the range of periods of the rheological noise caused by red cells passing through a capillary, cases (a) and (b) above, we have used values of both the mean capillary length and the mean velocity to calculate the average residence time of each cell in a capillary. Plyley et al. (1976) reported that the mean length of the capillary segment (i.e., the length of a capillary between two branching points) in the frog sartorius muscle was 0.85 mm. In our study, the overall mean velocity in capillary segments of the same muscle was 0.20 mm/sec. Since each red cell or slug of cells resided, on the average, not more than 4.25 sec (= 0.85/0.20) within a particular capillary segment, we estimate that this rheological noise does not include periods much greater than 4.25 sec. Occasionally, we have also observed red cells sticking to the capillary wall. During their contact with the wall, these cells caused an increased resistance to flow by partially obstructing the capillary lumen. In order to appreciate the contribution of this phenomenon to the overall rheological noise, we have measured both the incidence of cell sticking and the duration of the cell-wall contact in all 24 capillaries subjected to the velocity analysis described earlier. During 373 min of red cell flow the cells stopped 38 times for an average time interval of 1.65 sec (see Fig. 6). The longest interval was 4.5 sec. Referring to the analysis presented in the previous two paragraphs, one could explain the absence of correlation in the bands of T0-3 and 3-23 sec in terms of the rheological noise that is unique for each daughter capillary. But what about the slower uncorrelatable velocity variations in the band of 23-78 sec and, in some capillary pairs, in the band of 78-300 sec? Absence of correlation in these bands must also be caused by a process altering the red cell velocity separately in each daughter capillary. We believe, however, that this process cannot be theological noise, as discussed above, since that would introduce flow fluctuations that are much too fast to account for the slower variations which these bands represent. What then is this process'? We suspect that these slower variations are caused by changes in the resistance to flow mediated via changes in the luminal diameters of microvessels situated downstream from the branching point of the two capillaries. Referring to Fig. 5b, the slower variations represent only a few percent of the overall variations and therefore one would expect the changes in the luminal diameter to be also very small. In our video recordings of microvascular flow the number of
17
counts
11
0
2 duration
3
4
of c e l l - w a l l c o n t a c t
5
Is.el
FIG. 6. Histogram of the duration of the cell-wall contact. During the total of 373 min of red cell flow in 24 capillaries the red cells stuck to the capillary lumen 38 times for an average time interval of 1.65 sec.
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quality of the television picture was not good enough to measure such small changes; however, on several occasions, we were able to observe a region along a capillary where the lumen appeared to be narrower than that in the adjacent region. This "bottleneck" was situated either at the capillary entrance or several hundred micrometers away from it; its diameter was roughly 70% of the capillary diameter and its length was about one or two capillary diameters. Existence of similar "bottleneck" regions was reported by L~ibbers et al. (1979). They found that on electrical stimulation of capillaries in the rabbit mesentery blood flow was reduced, in 43 out of 63 capillaries, by a bulging of the nucleus of "special" endothelial cells in to the capillary lumen. Similar bulging was also found in endothelial cells of capillaries in the frog mesentery. These authors suggested that the bulging of specialized endothelial cells could mediate the regulation of capillary blood flow. Is it possible, then, that the slower velocity variations found in the present study were caused by the above mechanism? We do not know, but there certainly is evidence that endothelial cells in some tissues are capable of contraction. Ludatscher (1978) examined the ultrastructure of endothelial cells in venous capillaries and venules in human skin and found that some of these cells included an abundance of contractile filaments and showed, occasionally, bulging endothelial nuclei. The slower variations could also be caused by changes in the resistance to flow mediated via precapillary sphincters, or via changes in luminal diameter as described by Hauck et al. (1977). So far there has been no morphological evidence to show that sphincters exist in skeletal muscle; since we were not able to observe, in this preparation, any movement of the lumen at the capillary entrance, we suspect either that sphincters did not exist or that their activity was minimal. We also have not observed any of the funnel-shaped narrowings of the capillary lumen as reported by Hauck et al. (1977). These narrowings, 300 to 500 p,m away from the capillary branching, were seen in electrically stimulated capillaries in the rabbit mesentery. Assuming that the uncorrelatable velocity variations in the band of 23-78 sec, and possibly also in bands of 3-23 and 78-300 sec, provide indirect evidence for regulation of blood flow at the capillary level, the question arises: where does this regulation occur? One possibility is that the regulation takes place within each daughter capillary; the second possibility is that the regulation occurs in subsequent parts of the microvascular network such as venous capillaries or venules. In order to explain the absence of correlation between velocity variations in the two daughter capillaries, this second possibility must assume drainage of each daughter capillary into different venous capillaries or venules. If any resistance changes occurred in the venular part of the network, then the effect would most likely be uncorrelatable pressure changes at the outflow of each daughter capillary. Since the pressure at the inflow is the same for both capillaries, these uncorrelatable pressure changes would also result in uncorrelatable velocity fluctuations. In one experiment we were able to measure Vr~ in a rather special capillary pair: one of the capillaries rejoined the other after 300 p~m, thus forming a loop with identical inflow and outflow pressures for both microvessels. The values o f t for the different bands of periods, in this instance, were similar to those of Fig.
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5a and therefore we considered this as evidence for the first possibility, i.e., a separate regulatory process within each capillary. We conclude that in resting sartorius muscle in anesthetized frogs the arteriolar regulation of Vrbc Occurs predominantly on a minute-to-minute basis, and if any regulation occurs within individual capillaries or in subsequent parts of the microvascular network, this must be on a time scale of seconds only. Further, we estimate (Fig. 5b) that the minute-to-minute variations contribute about 18% to the overall biological variations and the second-to-second uncorrelatable variations as much as 52%. ACKNOWLEDGMENTS A part of the material in this paper was presented at the Second World Congress for Microcirculation, La Jolla, California, July 1979. This work was supported by the Studentship of the Medical Research Council awarded to K. Tyml and by a grant from the Ontario Heart Foundation awarded to A. C. Groom. The authors wish to express their great appreciation to Dr. C. Ellis for his helpful comments and stimulating discussions.
REFERENCES BURTON, K. S., AND JOHNSON, P. C. (1972). Reactive hyperemia in individual capillaries of skeletal muscle. Amer. J. Physiol. 223, 517-524. ERIKSSON, E., AND LlSANDER, B. (1972). Changes in precapillary resistance in skeletal muscle vessels studied by intravital microscopy. Acta Physiol. Scand. 84, 295-305. GENTRY, R. M., AND JOHNSON, P. C. (1972). Reactive hyperemia in arterioles and capillaries of frog skeletal muscle following microocclusion. Circ. Res. 31, 953-965. HAMMING, R. W. (1977). "Digital Filters," Prentice-Hall, Englewood Cliffs, N.J. HAUCK, G., WEIOELT, H., AND L~BaERS, D. W. (1977). Is there a possibility to influence blood flow in the capillary network of the mesentery of the rabbit by means of electrical stimulation? Bibl. Anat. 15(1), 448-451. JOHNSON, P. C., AND |NTAGLIETTA, M. (1976). Contributions of pressure and flow sensitivity to autoregulation in mesenteric arterioles. Amer. J. Physiol. 231(6), 1686-1698. JOHNSON, P. C., AND WAYLAND, H. (1967). Regulation of blood flow in single capillaries. Amer. J. Physiol. 212(6), 1405-1415. LI3BBERS, D. W., HAUCK, G., WEIGELT, H., AND ADDICKS, K. (1979). Contractile properties of frog capillaries tested by electrical stimulation. Bibl. Anat. 17, 3-10. LUDATSCHER, R. (1978). Ultrastructure of human dermal blood vessels with special reference to the endothelial filaments. Virchows Arch. B 27, 347-357. PLVLEY, M. J., SUTrlERLAND, G. J., AND GROOM, A. C. (1976). Geometry of the capillary network in skeletal muscle. Microvasc. Res. 11, 161-173. TYML, K., AND GROOM, A. C. (1980). Fourier transform analysis of periodic variations of red cell velocity in capillaries of resting skeletal muscle in frogs. Microvasc. Res. 20, 9-18. TVNL, K., AND SHEREHRIN, M. H. (1980). A method for on-line measurements of red cell velocity in microvessels using computerized frame-by-frame analysis of television images. Microvasc. Res. 20, 1-8. WIEDEMAN, M. P., TUMA, R. F., AND MAYROWITZ, H. N. (1976). Defining the precapillary sphincter. Microvasc. Res. 12, 71-75.