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Capillary diameter in rat heart in situ: Relation to erythrocyte deformability, O2 transport, and transmural O2 gradients
MICROVASCULAR
RESEARCH
12,259-214 (1976)
Capillary Diameter in Rat Heart In Situ: Relation to Erythrocyte Deformability, 0, Transport, and Transmural 0, Gradients LOUIS HENQUELL,’ University
of Rochester,
School 601 Elmwood
PAUL L. LACELLE,
AND CARL R. HONE
of Medicine Avenue,
Received
and Dentistry, Department Rochester, New York 14642
January
of Physiology,
13, 1976
The diameter of subepicardial capillaries was measured in stop-motion photomicrographs of normoxic rat hearts. Mean diameter over the whole cardiac cycle was 4.41 pm (0.09, SEM). Calculations indicate that mean diameter during systole is about 4 pm and during diastole is about 5 pm. The deformability ofraterythrocytes was evaluated by aspirating the cells into micropipets of various diameters. All cells traversed a 2.8~,um pipet at a mean AP of 0.17 mm Hg and a 2.5~pm pipet at a AP of 2.9 mm Hg. Below 2.5 pm, the pressure required to aspirate 100% of the cells increased linearly as the channel diameter decreased and reached 104 mm Hg at 1.9 ,um. Comparison of deformability data with frequency distributions of coronary capillary diameter indicates that all cells traverse all capillaries during diastole and traverse most superficial capillaries during systole. In the subendocardium, however, systolic tissue pressure is very high relative to erythrocyte deformability. Consequently, perfused capillaries should be compressed to the minimum thickness of an erythrocyte (about 1.8 ,um). Calculated pericapillary 0, gradients demonstrate that such narrow capillaries cannot sustain aerobic metabolism throughout the tissue. This is particularly true since capillary compression impedes erythrocyte entry, and thereby increases functional intercapillary distance. We conclude that: (1) Compression and narrowing of capillaries during systole can account for the transmural gradient in tissue pOz. (2) During diastole, capillary dimensions are perfectly matched to the dimensions and deformability of erythrocytes.
INTRODUCTION 0, gradients in cardiac muscle are extremely sensitive to the intracapillary as well as extracapillary portion of the diffusion path. This is true because PO’,,is high and capillary diameter is a significant fraction of extracapillary diffusion distance (Honig andBourdeau-Martini, 1973; Bourdeau-Martini etal., 1974).Information astocapillary diameter and its frequency distribution in the living heart is therefore essentialif 0, transport is to be quantitatively described. Recently, improvements in stop-motion microcinematography have made it possible to obtain well-focused pictures of surface capillaries in beating rat hearts in situ. 1 Present address: Universitk de Besancon, FacultC des Sciences and des Techniques, Laboratoire Physiologie Animale, 25030 Besancon Cedex, France. Copyright 0 1976 by Academic Press, Inc. Ail rights of reproduction in any form reserved. Printed in Great Britain
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de
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LACELLE
AND
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Observations to be described indicate that mean capillary diameter over the whole cardiac cycle is 4.41 pm (0.09, SEM) in the subepicardium. Frequency distributions of capillary diameter in relaxed hearts, and in hearts in rigor, are correlated with measurements of erythrocyte deformability. Results indicate that erythrocytes can transit all coronary capillaries during diastole. During systole, however, capillary diameter is decreased by myocardial tissue pressure, particularly in the deeper regions of the wall. Discussion develops the hypothesis that capillary compression accounts for the transmural gradient in tissue ~0, observed by Kirk and Honig (1964), Moss (1968), Winbury et al. (1971), and Whalen et al. (1973).
METHODS Techniques for stop-motion microcinematography of beating rat heart have been described in detail (Honig and Bourdeau-Martini, 1973; Bourdeau-Martini et al., 1974). Briefly, the heart is photographed by use of a 30-psec flash triggered by the film transport of a motion picture camera. In the rat, systole and diastole are about equal in duration. Consequently, pictures should be equally divided between the two phases of the cardiac cycle. We also photographed arrested hearts, in which vasodilation was fully developed. Arrest and vasodilation were produced by turning off the respirator. In some cases a clamp was applied to the A-V groove to prevent the capillaries from emptying. In other experiments no clamp was applied, and the heart was photographed about 15 min after respiratory arrest, when rigor was fully developed. Focused frames were projected onto a sheet of white paper to a final magnification of exactly 1000 x. Improved contrast with Ektachrome film was achieved by use of a green filter (Corning No. 4-97). A standard stage micrometer (Leitz) was used for calibration. Actual distances measured were on the order of 0.5 cm. Measurements were made along a single line drawn perpendicular to the long axis of the capillaries, in order to randomize error due to variation in diameter with capillary length. All measurements were made by one observer (L.H.) in ignorance of the identity of the material. Statistical analyses were performed on a desk calculator, programmed according to formulae in Snedecor and Cochran (1967). The ability of cells to enter and transit microvessels was measured by determining the percentage of cells which could be aspirated entirely into a micropipet of known diameter. Micropipets were right cylinders, whose diameters were constant for 50-100 pm from a smooth tip. Micropipets were calibrated with an eyepiece micrometer and a conventional microscope. The eyepiece was itself calibrated against a reference stage micrometer (Zeiss). A drop of rat blood was collected in a heparinized glass capillary tube. The sample was suspended in isotonic 2 mM Tris-NaCl buffer, pH 7.4, which contained 0.25 ‘A human albumin. Its osmolarity was 297 mOsm, and its viscosity was about the same as plasma. Experiments were performed within 2 hr after the blood was collected. Control experiments indicate that erythrocyte deformability did not change during this time. The sample was suspended in a microscope stage chamber at physiological pH, pOz, and temperature. Negative pressure required to aspirate cells was measured with a variable reluctance transducer and an ISD Whittaker digital manometer. Suction was controlled so that at least 1 set was required for entry.
CAPILLARY DIAMETER IN RAT HEART
261
RESULTS Characteristics of Original Data
In most experiments, capillaries were identified by the erythrocytes within them. Erythrocytes appear red on Ektachrome film against a light pink background of myoglobin. We shall refer to capillaries identified in this way as “red’capillaries. Representative red capillaries are shown in Figs. 1 c-f. Color contrast and transmitted light render the capillary edge more distinct in the projected images used for measurement than in black and white prints. In a few experiments, capillaries were identified not by their content of erythrocytes but rather by the optical properties of the endothelial cells themselves. On Ektachrome film, such capillaries appear almost white against a pink background of myoglobin. “White” capillaries afford better contrast and edge definition than red ones. Unfortunately, the white appearance was uncommon and was never observed in beating hearts.
FIG. 1. Photomicrographs of capillaries and venules on the surface of the rat heart. For full description, see text. a and b : white appearance of vessels in relaxed, anoxic hearts. C and V denote capillaries and venules. The two large vessels in a are veins. The entire length of a vessel in the focused field can be observed, and the capillary edge is well defined. c-f: red capillaries. c: relaxed anoxic heart. Note that there are few gaps in the erythrocyte columns. Capillary diameter is about the same as in a and b. d: anoxic heart in rigor. Capillaries are narrower than in a-c. Arrows indicate gaps between individual erythrocytes. Note also the long capillary segments which contain no erythrocytes. e and f: beating hearts. Capillaries in e are narrow and gaps in the erythrocyte columns are present; see arrows. Capillaries in fare wider and better filled with erythrocytes. It is likely that e and f were taken in systole and diastole, respectively.
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AND
FIGURE 1. Continued
HONIG
CAPILLARY
DIAMETER
IN
RAT
HEART
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LACELLE
FIGURE
AND
HONIG
1. Continued
Figure la illustrates white capillaries (C), venules (V), and two small veins. Some capillaries join others to form a venule which then joins a vein, whereas others join a small vein directly. Note that in the lower right there are two short anastomoses between a capillary and the adjacent vein. Anastomoses are also present between capillaries. Anastomoses are particularly common at the apex of the heart, where they break the capillaries up into rather short segments or loops. Figure 1b illustrates white capillaries at the apex. In general, the diameter of an anastomosis is smaller than that of the capillary from which it arises. Note in Figs. la and lb that the entire length of a capillary in the focused field is discernable. Figure Ic illustrates the appearance of red capillaries in a relaxed, anoxic heart. A clamp was applied to the A-V groove to prevent blood from leaving the capillaries. The capillaries are distended, and the column of erythrocytes within them is nearly continuous. Figure Id illustrates capillaries in an anoxic heart in rigor. The forces acting on the capillaries are analogous to those during systole. No clamp was applied to the A-V groove, so the capillaries were free to empty. Capillary diameter is noticeably smaller than in Figs. la-c. In some places, gaps are present between individual erythrocytes; see arrows. Elsewhere, long capillary segments are empty of erythrocytes. Figure le was obtained in a beating heart. Like the heart in rigor, the capillaries are narrow, with many segments devoid of erythrocytes; see arrows. Figure If was also obtained from a beating heart. Capillary diameter is larger than in d and e but smaller than in a<. As in the relaxed anoxic heart, there are long continuous columns of
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erythrocytes with only a few short gaps. It is possible that e and f were taken in systole and diastole, respectively. Mean Capillary Diameter
The mean diameter of white capillaries was slightly larger than red; see Table 1. This might be expected, since measurements of white capillaries include the thickness of the endothelial cells. The difference was only0.2pm, however, and was not statistically significant. Comparison of red and white capillary diameters indicates that measurements on red capillaries are of acceptable precision. All further observations in this paper are based on red capillaries. Note in Table 1 that mean capillary diameter is significantly larger in the beating heart than in the heart in rigor. In contrast, mean capillary diameter in the beating heart is significantly smaller than in the relaxed, anoxic heart. TABLE MEAN
DIAMETER
1
OF SUBEPICARDIAL
CAPILLARIES
Mean diameter Cm)
SD
IN THE RAT
n
Rigor Beating heart
4.12 4.41
1.03 1.10
95 167
Relaxed red capillaries
5.31
1.38
69
Relaxed white capillaries
5.52
1.37
84
P
+---, 10.05 t--l --I
In samples from seven animals, mean capillary diameter was not significantly different in right and left ventricles and in large and small animals (range, 155-520 g). However, observations on a larger population are necessary to exclude a difference on the order of 0.5 pm. Frequency Distributions
Frequency distributions of individual diameter measurements are Gaussian; see Fig. 2. However, the curve for the beating heart (panel C) has a flatter top and fewer observations in its flanks than is expected for the normal distribution. This kurtosis is statistically significant (P < 0.05). The maximum frequency for hearts in rigor (panel A) corresponds to the class 3-4 pm. There are few observations in that class in the distribution for anoxic, relaxed hearts (panel B). The peak frequency in panel B corresponds to the class 5-6 pm. The flat top in panel C contains the classes 3-4 and 5-6 pm, suggesting that it is essentially a composite of panels A and B. The distributions in Fig. 2 are shown as cumulative probability plots in Fig. 3, curves 1,2, and 4. In this form they can be more easily correlated with the properties of erythrocytes.
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HENQUELL,
Dimensions and Deformability
LACELLE
AND
HONIG
of Erythrocytes
The rat erythrocyte is smaller than that of the human. In suspension its mean volume is 61 pm3, and its mean diameter is 6.8 ,um. Its calculated surface area is 93 rum*. The mean pressure gradient (dP) required to force all cells through a 2.8~pm pipet is only 0.17 mm Hg. As shown in Fig. 4, filled circles, this pressure gradient is less than
CAPILLARY DIAMETER - u
2. Frequencyhistograms of capillarydiameter.A: heartsin rigor: B: redcapillaries in relaxed, anoxichearts;C: beatinghearts.Thedistributionin C hascharacteristics of both A andB. FIG.
1 mm Hg for channels ~2.6 pm. Below 2.5 pm, the requisite pressure gradient rises steeply and linearly from 9.6 mm Hg at 2.45 pm to 104 mm Hg at 1.9 ,um. Mean cell length in the 2.4~pm pipet was 11.2 pm. The channel diameter at which AP rises represents the smallest right cylinder through which a cell can pass without increasing its membrane area. This critical diameter is 2.45 pm for rat erythrocytes. In living microcirculation, the pressuregradient from arteriole to venule is lessthan
10 mm Hg (Smaje et al., 1970). It is therefore useful to know the percentage of erythrocytes which can traverse channels of various diameters when the pressuregradient is restricted to this physiological range. This information is shown by the open circles in Fig. 4. If erythrocyte behavior in uivo is the sameas in vitro, 92% of the cells should
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transit 2.5-pm capillaries. It is significant that only 2 % of the capillaries were smaller than 2.5 pm in relaxed hearts (refer to Fig. 3, curve 4). Judging from hearts in rigor (Fig. 3, curve l), about 13 % of subepicardial capillaries are narrower than 2.5 pm during systole. We conclude that all cells can enter all capillaries during diastole and that contraction has little effect on entry of erythrocytes into surface capillaries.
I
2
3
4
CAPILLARY
5
6
DIAMETER
7 -
8
9
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u
FIG. 3. Cumulative probability plots of the data shown in Fig. 2. Curve 1: hearts in rigor; curve 2: beating hearts; curve 4: relaxed, anoxic hearts; curve 3: sum of curves 1 and 4.
iii 2 Y E O 1.6 2.0 2.1 2.2 2.3 2.4 2.5 4 MICROPIPETTE
2.6
2.7 2.8
DIAMETER
FIG. 4. The left ordinate indicates negative pressures required to aspirate 100% of the erythrocytes into right-cylindrical glass micropipets whose diameters are shown on the abscissa. Open circles indicate percentage of cells which can be aspirated at pressures less than 10 mm Hg.
The situation within the and Honig, 1964a; Armour mechanical properties of the mural capillary compression
wall is complicated by systolic tissue pressure (Kirk and Randall, 1971). This pressure is opposed by the erythrocytes. The magnitude and consequences of intraare considered below. DISCUSSION
Criticism of Method
Accuracy of capillary diameter measurements is chiefly limited by definition of the capillary edge. In anoxic, arrested hearts, we occasionally observed capillaries with
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particular clarity. These white capillary appearances seem to depend on the optical properties of the endothelial cells. We cannot explain what enables us to visualize the capillaries in this way in some experiments but not in others. Nevertheless, the phenomenon is useful because it permits us to identify the limits of the capillary wall very precisely. When we compare diameters of white and red capillaries for the same experimental conditions, no significant difference is observed in mean, variance, or frequency distribution. We conclude from this that the accuracy of our usual measurements on red capillaries is not limited by definition of the capillary edge. The reader should bear in mind that the values we report are means with respect to position along the capillary. Eriksson and Myrhage (1972) report that capillary diameter in living rat skeletal muscle increases by about 1 pm from the arterial to the venous end. Inability to control for this doubtless contributed to the variability we observed. All our measurements were made on longitudinally oriented capillaries. In interpreting them we assume that the capillary cross section is circular. Photomicrographs of capillary casts indicate that this is true of the relaxed heart (Bassingthwaighte et al., 1974). Whether the cross section is circular or eliptical in systole depends on whether compressive forces in the myocardium are uniform in all directions. This appears to be the case for the superficial portion of the wall on which we made our observations (Kirk and Honig, 1964a). The most important limitation of our method is that we can observe capillaries no deeper than 20 pm from the epicardial surface. Although capillary diameter is the same throughout the dead heart (Bassingthwaighte et al., 1974), in the beating heart, compressive forces acting on deep capillaries are considerably greater than those which act on superficial ones (Kirk and Honig, 1964a; Armour et al., 1971). Consequently, our measurements do not apply to systolic capillary diameter deep within the wall. Mean Capillary Diameter under Various Circumstances
The average internal diameter of coronary capillaries postmortem has been measured in silicone-rubber casts. Sobin and Tremer (1972) reported a range of 2-7 pm, with a mean of about 4 pm in various animal species. Bassingthwaighte and co-workers (1974), in a carefully controlled study of canine coronary capillaries, obtained about the same result. They found, however, that procedures used to clear the casts of tissue cause significant shrinkage. When corrected for this artifact, mean capillary diameter was 5.5 pm. They pointed out that high intracapillary pressure and hypoxia during perfusion with silicone-rubber could have increased capillary diameter and suggested that the true value in viva may be less than 5.5 pm. The diameter of coronary capillaries is about the same in the dog and the rat (Sobin, personal communication). Our results can therefore be compared with those of Bassingthwaighte and co-workers. We find mean capillary diameter to be 5.3 pm in anoxic, arrested, relaxed hearts in which capillary pressure is maintained by preventing venous outflow. If measurements on capillaries during rigor, and in relaxed hearts, accurately describe diameters in systole and diastole, the frequency distribution obtained by pooling these measurements should reproduce the distribution obtained for the beating heart. Note in Fig. 3, however, that the pooled data (curve 3) lie to the right of curve 2 (beating heart). In addition, curve 2 does not have a long upper tail. This upper tail could represent capillaries injured by anoxia. If the difference between curves 2 and 3 is
CAPILLARY
DIAMETER
IN RAT
HEART
269
indeed due to anoxic damage, mean capillary diameter in diastole should be about 0.3 pm less than mean diameter in anoxic, relaxed hearts. We conclude that the mean capillary diameter is about 5 pm in diastole. This figure is almost identical to mean capillary diameter in living rat skeletal muscle at rest (Eriksson and Myrhage, 1972). The only measurements of capillary diameter in living heart other than our own are those of Tillmanns et al. (1974). They report diastolic capillary diameter in dog to be 6.3 f 0.08 pm SEM. Their value is probably too large, for it is significantly greater than that of Bassingthwaighte et al. (1974) for maximum capillary diameter in anoxic dog hearts. The overestimate could be accounted for by insufficiently sharp definition of the capillary edge in their tine photomicrographs. Figure 3, curve 4 demonstrates that there are virtually no capillaries less than 2.5 pm in diameter in relaxed, anoxic hearts. It is therefore likely that observations made in diastole do not contribute significantly to the lower tail of the ogive for the beating heart (curve 2). Note also that the lower quartile of the distributions for rigor (curve 1) and for the beating heart are superimposable. On this evidence, mean capillary diameter in systole should be about 4 pm in the superficial regions of the wall. Since systolic tissue pressure is greater than 100 mm Hg in the subendocardium (Kirk and Honig, 1964a; Armour and Randall, 1971), capillaries there should be compressed to the minimum thickness of a rat erythrocyte (about 1.8 pm). We conclude that capillary diameter during systole decreases about 1 pm in the subepicardium and 3 jlrn in the subendocardium. The extent to which capillary segments devoid of erythrocytes narrow during systole is unknown, but if there is free egress of plasma, as implied by observations of Tillmanns et al. (1974), collapse could be complete. Quite recently, actomyosin has been identified in endothelium by means of immunofluorescence (Becker and Nachman, 1973) and thin filaments of actin have been observed attached to the plasmalemma of coronary endothelial cells (Yohro and Burnstock, 1973). It is therefore possible that active changes in capillary diameter occur in addition to passive changes induced by cardiac-muscle contraction. Such changes could be of considerable importance, for they would affect diffusion conditions during diastole. Capillary
Diameter and Erythrocyte
Deformability
The high vo, of myocardium relative to blood flow necessitates a large number of perfused capillaries per volume of tissue. On the other hand, the ratio of capillary blood volume to tissue volume must be small in the interest of efficient contraction. The chief adaptation to these stringencies is small capillaries; 99 ‘A of the capillaries in the beating rat heart are smaller than the mean diameter of an erythrocyte. Erythrocytes can traverse small capillaries because they are highly deformable. The foregoing has been known since Krogh’s description of blood flow in capillaries more than a half a century ago. Nevertheless, our study appears to be the first attempt to quantify the relation between the size and properties of erythrocytes and the dimensions of living capillaries. We find that nature has achieved a perfect match except for complications due to cardiac contraction. All rat erythrocytes can transit a 2.8~pm pipet, and about 92% can transit a 2.5-pm pipet at pressures less than 10 mm Hg. During diastole, almost no capillaries less than 2.5 pm in diameter should exist anywhere in rat myocardium. Systole is equally as long as diastole in the rat. Judging from measurements in dogs (Kirk and Honig, 1964a; Armour and Randall, 1971), peak systolic tissue pressure
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greatly exceeds endocapillary pressure, except for the most superficial regions of the wall. Capillary compression is opposed by the mechanical properties of erythrocytes. However, erythrocytes offer little resistance to deformation until capillary diameter reaches 2.5 pm. At that point, the erythrocyte reaches the maximum length attainable without an increase in the area of its membrane. Since compressive forces in tissue increase from 0 at the epicardial surface to more than 100 mm Hg in the subendocardium, a transmural gradient in mean capillary diameter is created by the transmural tissue-pressure gradient. The minimum capillary diameter in the subendocardium should be about 1.8 pm, the minimum thickness of a rat erythrocyte. Capillary compression has two major effects on O2 transport: (1) It hinders entry of erythrocytes into capillaries. As shown in Fig. 4, this hinderance should parallel the transmural gradients in tissue pressure and capillary diameter. Hinderance to entry produces gaps between individual erythrocytes and long capillary segments devoid of erythrocytes. These changes result in regions of tissue in which the extracapillary diffusion path is very long. (2) The 0, content of the capillary per unit length is decreased even where erythrocytes are present, because these latter are deformed into long thin cylinders. Thus, tissue pressure decreases the volume of the 0, source and increases the volume of the sink at the very time r’,, is at a maximum. Calculated pericapillary O2 gradients indicate that the foregoing accounts for the transmural gradient in tissuep0,. Capillary Radius and O2 Gradients
The mean radius of a perfused capillary is about 30% of the mean tissue-cylinder radius in the beating rat heart, but is only 4% of the tissue-cylinder radius in resting rat skeletal muscle (Honig and Bourdeau-Martini, 1973). Because coronary capillaries are so large a fraction of the total diffusion distance their size has a profound effect on 0, transport. An appreciation of the quantitative significance of capillary radius, and of the interaction between capillary radius and capillary spacing, can be gained by use of the Krogh equation; see Fig. 5. In these calculations, Krogh’s 0, diffusion coefficient was used and the po’,, of the rat heart was assumed to be 6.6 x 10m3ml/g/set (BourdeauMartini et al., 1974). The abscissa indicates distance from the center of the capillary. The origin of each isopleth, referenced to the abscissa, indicates the locus of the capillary wall. 2R denotes the center-center distance between capillaries. Each isopleth describes the radial decrement in p0, from the capillary wall for the indicated capillary diameter and spacing. Capillary p02 was set at mean venous p0, in order to simulate conditions at the low end of the longitudinal intracapillary 0, gradient. If this gradient is roughly exponential, the computed tissue O2 gradients approximate conditions in a substantial fraction of the myocardium. Section A illustrates the gradients for normal paOz, coronary blood flow, mean endcapillary pO1, and mean capillary spacing. Note especially that O2 gradients are much steeper for small capillaries. The minimum tissue pOz for a 2-pm capillary is almost 20 mm Hg lower than for an 8-pm one. According to Chance et al. (1973), mitochondrial respiration is not compromised until tissue p0, falls below 0.1 mm Hg. Consequently, even the smallest capiIlaries we observed appear to be sufficient to support aerobic metabolism for these conditions. One of the many limitations of our analysis, however, is that we average PO’,,over the cardiac cycle. If Ijo2 during systole is 50 ‘A greater than average Tioz, some of the tissue supplied by capillaries less than 2.5 pm in diameter
271
CAPILLARY DIAMETER IN RAT HEART
would sustain an 0, debt. Only about 15 % of the capillaries are that small in the subepicardium. However, the percentage of capillaries ~2.5 pm should increase progressively with depth and approach 100 % in the subendocardium. Presumably, 0, debts incurred during systole can be repaid during diastole under normal circumstances. The foregoing analysis neglects the fact that large variations in flow velocity (Eriksson and Myrhage, 1972; Tillmanns et al., 1974) and capillary length (Bassingthwaighte et al., 1974) exist. These variations give rise to a frequency distribution of end-capillary
25 -
2R
-25
= 25~
I” 20: I
15-
IO
@ C
2
36” 64 -20 -155
I 0
2
4
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MICRONSFROM CENTER OF CAPILLARY FIG. 5. Interaction of capillary diameter, capillary spacing, and capillarypOz on calculated gradients of tissuepOz. 2R denotes the center-to-center distance between capillaries. Numerals beside isopleths indicate capillary diameter. See text for description and analysis.
pOZ, with many values less than half of the mean venousp0, (Grunewald and Lubbers, 1975). Gradients in Fig. 5d are computed for the same conditions as in Fig. 5a except that end-capillary pOZ is assumed to be 10 mm Hg. Note that about half of the tissuecylinder cross section would be anoxic even at the mean diameter of subepicardial capillaries. Conversely, no anoxia whatever would exist even around narrow, widely spaced capillaries if capillarypo, were 40-50 mm Hg, as might be the case at the arterial end of the longitudinal 0, gradient. In previous reports we have emphasized that a Gaussian distribution of intercapillary distances exists (Honig and Bourdeau-Martini, 1973; Bourdeau-Martini et al., 1974). Figure 5c illustrates gradients around widely spaced capillaries; all other conditions are as in a. Even if vo, is averaged over the cardiaccycle, some of the tissue supplied by capillaries less than 3 pm in diameter would be anoxic. The amount of anoxic tissue depends on the frequency distributions of critical parameters. In the normal rat heart only about 20 % of the superficial capillaries are spaced as widely as in Fig. 5c and only about 25 ‘A of the subepicardial capillaries are narrower than 3 pm. The frequency dis-
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tribution of end-capillary pOZ is not presently available. Obviously, hypoxia should be much more extensive in the subendocardium, where during systole the frequency distribution of capillary diameter should be shifted to the left, and that of intercapillary distance to the right. Figure 5b illustrates conditions in moderate hypoxia. lioZ is the same as in a, but the mean intercapillary distance is assumed to be 3 pm shorter. Such a decrease in intercapillary distance has actually been observed in the living heart (Honig and BourdeauMartini, 1973; Bourdeau-Martini et al., 1974). Tissue 0, gradients are not as steep as in a and c because the capillaries are more closely spaced. ~0, at the capillary wall is so low, however, thatp0, goes to 0 in portions of the tissue supplied by capillaries less than 3.5 pm in diameter. From Fig. 3, we estimate that about 50 % of the subepicardial capillaries are less than 3.5 pm in diameter during systole, whereas only about 20 % are less than 3.5 ,um during diastole. We conclude that under hypoxic conditions the decrease in capillary diameter during systole has important consequences for 0, transport. Note that the small size of coronary capillaries limits the effectiveness of capillary recruitment in compensating for hypoxia: If all capillaries were 4 pm wide, aerobic respiration would be possible throughout. Recruitment is nonetheless essential. Figure 5d illustrates the effect of hypoxia if recruitment were impaired, as, for example, in hypertrophy (manuscript in preparation). Conditions are the same as in Fig. 5b except that 2R is 3 ym larger. Anoxia would exist in some of the tissue supplied by capillaries smaller than about 6 ym. This includes about 90 % of the capillaries in the myocardium, even in diastole. In recent years, highly sophisticated models of 0, transport have been developed based on iterative computing techniques (Grunewald, 1973). The magnitude of the interaction of diffusion distance and capillary diameter indicates that the frequency distributions of both parameters, and fluctuations in the distributions during the cardiac cycle, must be included in such models.
The Transmural Gradient in Tissue pO1 By use of 0, electrodes, ~0, in the subendocardium has been found to be about half of that in the subepicardium (Kirk and Honig, 1964b; Moss, 1968; Winbury et al., 1971; Whalen et al., 1973). A corresponding transmural gradient in the ratio of NAD+ to NADH has been measured by direct chemical assay (Hayashi et al., 1974). The following explanations for the transmural O2 gradient have been offered: (1) diffusional shunting (Bassingthwaighte et al., 1974); (2) low subendocardial blood flow (Kirk and Honig, 1964b); and (3) high subendocardial vo’,, (Winbury et aE., 1971). 1. Judging from the behavior of tritiated water, a significant diffusional shunt at the level of the capillaries is unlikely at normal coronary flow (Yipintsoi and Bassingthwaighte, 1970). This is in accord with the fact that coronary capillaries are almost exclusively concurrent (Tillmanns et al., 1974). However, Bassingthwaighte et al. (1974) point out that the arrangement of conducting vessels is consistent with 0, diffusion from arteries to veins. Though more experiments to this point are required, no evidence of a diffusional shunt for 0, could be obtained in isolated rat hearts (Huhmann et al., 1967). 2. Early studies based on depot clearance revealed an apparent transmural gradient in coronary flow (Kirk and Honig, 1964b). Though average subendocardial
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CAPILLARY DIAMETER IN RAT HEART
flow may indeed be low in certain disease states (Kjekshus, 1973), evidence based on microspheres indicates that the ratio of epicardial to endocardial flow is close to unity in the normal heart (Domenech et al., 1969; Kjekshus, 1973). 3. When a coronary artery is occluded, tissue pOz estimated with 0, cathodes falls most rapidly in the subendocardium, suggesting that tie, is greatest in this region (Winbury et al., 1971). However, several other interpretations are possible, and high ro, in the subendocardium is inconsistent with the fact that longitudinal tension in endocardial muscle fibers is about a third less than in epicardial fibers (Armour and Randall, 1971). Even if vo, were greater in the subendocardium, the effect of this on tissue ~0, should be compensated by the short diastolic diffusion distances characteristic of this region (Myers and Honig, 1964). We conclude that none of the foregoing explanations is satisfactory. Figures Id and le demonstrate that contraction excludes erythrocytes from long segments of coronary capillaries. Since the 0, capacity of an empty capillary is negligible, the distance between functional capillary segments increases during systole. The locus of a collapsed capillary segment is random and therefore different from beat to beat. The diameters of capillaries which contain erythrocytes are determined by the relationship between tissue pressure and erythrocyte deformability; refer to Fig. 4. These effects of contraction increase from the epicardium to the endocardium, in parallel with the tissue-pressure gradient. Consequently, the volume of tissue which a capillary can service is decreased at the very time when blood flow is lowest, voz is highest, and regions of long intercapillary distance exist. As shown in Fig. 5, this combination of conditions should produce anoxia in a substantial portion of the tissue. In agreement with this prediction, Whalen and co-workers (1973) reported that in cat hearts, ~0, was between 0 and 5 mm Hg in 27 % of the subepicardial cells and in 61% of the cells more deeply situated. We conclude that the transmural gradient in tissue pOz is best explained by the effect of tissue pressure on the dynamics of the coronary capillary circulation. ACKNOWLEDGMENTS We thank Mr. William H. DeVeer for help with the photography. Mr. James L. Frierson provided expert technical assistance. This research was supported by Grants HL-03290, HL-16421, and HL-18208 from the National Institutes of Health and by a grant-in-aid from the Genesee Valley Heart Association. REFERENCES 1.
J. A.,
ARMOUR,
Amer.
J. Physiol.
AND
W. C. (1971). Canine left ventricular intramyocardial
RANDALL,
pressures.
220,1833-1839.
2.
BASSINGTHWAIGHTE, J. B., YIPINTSOI, T., AND HARVEY, R. B. (1974). Microvasculature of the dog left ventricular myocardium. Microvusc. Res. 7,229-249. 3. BECKER, C. G., AND NACHMAN, R. L. (1973). Contractile proteins of endothelial cells, platelets, and smooth muscle. Amer. J. Pathol. 71, l-18. 4. BOURDEAU-MARTINI, J., ODOROFF, C. L., AND HONIG, C. R. (1974). Dual effect of oxygen on magnitude and uniformity of coronary intercapillary distance. Amer. J. Physiol. 226, 800-810. 5. CHANCE, B., OSHINO, N., SUGANO, T., AND MAYEVSKY, A. (1973). Basic principles of tissue oxygen determination from mitochondrial signals. Adv. Exper. Med. Biol. 37,277-292. 6. DOMENECH, R. J., HOFFMAN, J. I. E., NOBLE, M. I. M., SAUNDERS, K. B., HENSON, J. R., AND SUBIJANTO,
S. (1969).
Total
and
regional
coronary
blood
flow
spheres in conscious and anesthetized dogs. Circ. Res. 25,581-596.
measured
by radioactive
micro-
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AND
HONIG
7. ERIKSSON,E., AND MYRHAGE, R. (1972). Microvascular dimensions and blood flow in skeletal muscle. Acta Physiol. &and. 86,221-222. 8. GRUNEWALD, W. (1973). Computer calculation for tissue oxygenation and the meaningful presentation of the results. Adv. Exper. Med. Biol. 37, 783-792. 9. GRUNEWALD, W. A., AND LUBBERS, D. W. (1975). Die Bestimmung der intracapilliiren HbO,Sgttigung mit einer kryo-mikrofotometrischen Method angewandt am Myokard des Kaninchens. Pflcger’s
Arch.
353,255-273.
10. HAYASHI, A., TAKANO, S., HASHIKAWA, T., AND ABIKO, Y. (1974). Redox state of nicotinamideadenine dinucleotide in the inner and outer layers of canine left ventricle, and effects of coronary dilators on the redox state. Japan J. Pharmacol. 24,763-770. 11. HONIG, C. R., AND BOURDEAU-MARTINI, J. (1973). Role of 0, in control of the coronary capillary reserve. Adv. Exper. Med. BioI. 39, 55-71. 12. HUHMANN, W., NIESEL, W., AND GROTE, J. (1967). Untersuchungen iiber die Bedingungen fiir die Sauerstoffsversorgung des Myokards an perfundierten Rattenherzen. Pfliiger’s Arch. 294,250-255. 13. KIRK, E. S., AND HONIG, C. R. (1964a). An experimental and theoretical analysis of myocardial tissue pressure. Amer. J. Physiol. 207, 361-367. 14. KIRK, E. S., AND HONIG, C. R. (1964b). Nonuniform distribution of blood flow and gradients of oxygen tension within the heart. Amer. J. Physiol. 207,661-668. 15. KJEKSHUS, J. K. (1973). Mechanism for flow distribution in normal and ischemic myocardium during increased ventricular preload in the dog Circ. Res. 33,489-499. 16. KROGH,A. (1919).Thesupplyof oxygen to thetissuesandtheregulationofthecapillarycirculation. J. Physiol.
(London)
52,457-474.
17. LACELLE, P., AND WEED, R. I. (1971). The contribution of normal and pathologic erythrocytes to blood rheology. Prog. Hematol. 7,1-3 1. 18. Moss, A. J. (1968). Intramyocardial oxygen tension. Cardiovasc. Res. 3, 314-318. 19. MYERS, W. W., AND HONIG, C. R. (1964). Number and distribution of capillaries as determinants of myocardial oxygen tension. Amer. J. Physiol. 207,653-660. 20. SMAJE, L., ZWEIFACH, B. W., AND INTAGLIETTA, M. (1970). Micropressure and capillary filtration coefficients in single vessels of the cremaster muscle of the rat. Microvasc. Res. 2, 96-l 10. 21. SNEDECOR,G. W., AND COCHRAN, W. G. (1967). “Statistical Methods,” pp. 84-88 and 1044107. Iowa State University Press, Ames, Iowa. 22. SOBIN, S., AND TREMER, H. M. (1972). Diameter of myocardial capillaries. Microvasc. Res. 4, 330-331. 23. TILLMANNS, H., IKADA, S., HANSEN, H., JONNALAGEDDA, S., SARMA, M., FAUVEL, J. M., AND BING, R. J. (1974). Microcirculation in the ventricle of the dog and turtle. Circ. Res. 34, 561-569. 24. WHALEN, W. J., NAIR, P., AND BUERK, D. (1973). Oxygen tension in beating cat heart in situ. In “Oxygen Supply” (M. Kessler, D. F. Bruley, L. C. Clark, Jr., D. W. Liibbers, I. A. Silver, and J. Strauss, eds.), pp. 199-201. University Park Press, Baltimore, Maryland. 25. WINBURY, M. M., HOWE, B. B., AND WEISS,H. R. (1971). Effect of nitroglycerine and dipyridamole on epicardial and endocardial oxygen tension-further evidence for redistribution of myocardial blood flow. J. Pharmacol. Exper. Therap. 176, 184-199. 26. YIPINTSOI, T., AND BASSINGTHWAIGHTE,J. B. (1970). Circulatory transport of iodoantipyrine and water in the isolated dog heart. Circ. Res. 27,461-477. 27. YOHRO, T., AND BURNSTOCK, G. (1973). Filament bundles and contractility of endothelial cells in coronary arteries. 2. Zellforsch. 138, 85-95.
RESEARCH
12,259-214 (1976)
Capillary Diameter in Rat Heart In Situ: Relation to Erythrocyte Deformability, 0, Transport, and Transmural 0, Gradients LOUIS HENQUELL,’ University
of Rochester,
School 601 Elmwood
PAUL L. LACELLE,
AND CARL R. HONE
of Medicine Avenue,
Received
and Dentistry, Department Rochester, New York 14642
January
of Physiology,
13, 1976
The diameter of subepicardial capillaries was measured in stop-motion photomicrographs of normoxic rat hearts. Mean diameter over the whole cardiac cycle was 4.41 pm (0.09, SEM). Calculations indicate that mean diameter during systole is about 4 pm and during diastole is about 5 pm. The deformability ofraterythrocytes was evaluated by aspirating the cells into micropipets of various diameters. All cells traversed a 2.8~,um pipet at a mean AP of 0.17 mm Hg and a 2.5~pm pipet at a AP of 2.9 mm Hg. Below 2.5 pm, the pressure required to aspirate 100% of the cells increased linearly as the channel diameter decreased and reached 104 mm Hg at 1.9 ,um. Comparison of deformability data with frequency distributions of coronary capillary diameter indicates that all cells traverse all capillaries during diastole and traverse most superficial capillaries during systole. In the subendocardium, however, systolic tissue pressure is very high relative to erythrocyte deformability. Consequently, perfused capillaries should be compressed to the minimum thickness of an erythrocyte (about 1.8 ,um). Calculated pericapillary 0, gradients demonstrate that such narrow capillaries cannot sustain aerobic metabolism throughout the tissue. This is particularly true since capillary compression impedes erythrocyte entry, and thereby increases functional intercapillary distance. We conclude that: (1) Compression and narrowing of capillaries during systole can account for the transmural gradient in tissue pOz. (2) During diastole, capillary dimensions are perfectly matched to the dimensions and deformability of erythrocytes.
INTRODUCTION 0, gradients in cardiac muscle are extremely sensitive to the intracapillary as well as extracapillary portion of the diffusion path. This is true because PO’,,is high and capillary diameter is a significant fraction of extracapillary diffusion distance (Honig andBourdeau-Martini, 1973; Bourdeau-Martini etal., 1974).Information astocapillary diameter and its frequency distribution in the living heart is therefore essentialif 0, transport is to be quantitatively described. Recently, improvements in stop-motion microcinematography have made it possible to obtain well-focused pictures of surface capillaries in beating rat hearts in situ. 1 Present address: Universitk de Besancon, FacultC des Sciences and des Techniques, Laboratoire Physiologie Animale, 25030 Besancon Cedex, France. Copyright 0 1976 by Academic Press, Inc. Ail rights of reproduction in any form reserved. Printed in Great Britain
259
de
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Observations to be described indicate that mean capillary diameter over the whole cardiac cycle is 4.41 pm (0.09, SEM) in the subepicardium. Frequency distributions of capillary diameter in relaxed hearts, and in hearts in rigor, are correlated with measurements of erythrocyte deformability. Results indicate that erythrocytes can transit all coronary capillaries during diastole. During systole, however, capillary diameter is decreased by myocardial tissue pressure, particularly in the deeper regions of the wall. Discussion develops the hypothesis that capillary compression accounts for the transmural gradient in tissue ~0, observed by Kirk and Honig (1964), Moss (1968), Winbury et al. (1971), and Whalen et al. (1973).
METHODS Techniques for stop-motion microcinematography of beating rat heart have been described in detail (Honig and Bourdeau-Martini, 1973; Bourdeau-Martini et al., 1974). Briefly, the heart is photographed by use of a 30-psec flash triggered by the film transport of a motion picture camera. In the rat, systole and diastole are about equal in duration. Consequently, pictures should be equally divided between the two phases of the cardiac cycle. We also photographed arrested hearts, in which vasodilation was fully developed. Arrest and vasodilation were produced by turning off the respirator. In some cases a clamp was applied to the A-V groove to prevent the capillaries from emptying. In other experiments no clamp was applied, and the heart was photographed about 15 min after respiratory arrest, when rigor was fully developed. Focused frames were projected onto a sheet of white paper to a final magnification of exactly 1000 x. Improved contrast with Ektachrome film was achieved by use of a green filter (Corning No. 4-97). A standard stage micrometer (Leitz) was used for calibration. Actual distances measured were on the order of 0.5 cm. Measurements were made along a single line drawn perpendicular to the long axis of the capillaries, in order to randomize error due to variation in diameter with capillary length. All measurements were made by one observer (L.H.) in ignorance of the identity of the material. Statistical analyses were performed on a desk calculator, programmed according to formulae in Snedecor and Cochran (1967). The ability of cells to enter and transit microvessels was measured by determining the percentage of cells which could be aspirated entirely into a micropipet of known diameter. Micropipets were right cylinders, whose diameters were constant for 50-100 pm from a smooth tip. Micropipets were calibrated with an eyepiece micrometer and a conventional microscope. The eyepiece was itself calibrated against a reference stage micrometer (Zeiss). A drop of rat blood was collected in a heparinized glass capillary tube. The sample was suspended in isotonic 2 mM Tris-NaCl buffer, pH 7.4, which contained 0.25 ‘A human albumin. Its osmolarity was 297 mOsm, and its viscosity was about the same as plasma. Experiments were performed within 2 hr after the blood was collected. Control experiments indicate that erythrocyte deformability did not change during this time. The sample was suspended in a microscope stage chamber at physiological pH, pOz, and temperature. Negative pressure required to aspirate cells was measured with a variable reluctance transducer and an ISD Whittaker digital manometer. Suction was controlled so that at least 1 set was required for entry.
CAPILLARY DIAMETER IN RAT HEART
261
RESULTS Characteristics of Original Data
In most experiments, capillaries were identified by the erythrocytes within them. Erythrocytes appear red on Ektachrome film against a light pink background of myoglobin. We shall refer to capillaries identified in this way as “red’capillaries. Representative red capillaries are shown in Figs. 1 c-f. Color contrast and transmitted light render the capillary edge more distinct in the projected images used for measurement than in black and white prints. In a few experiments, capillaries were identified not by their content of erythrocytes but rather by the optical properties of the endothelial cells themselves. On Ektachrome film, such capillaries appear almost white against a pink background of myoglobin. “White” capillaries afford better contrast and edge definition than red ones. Unfortunately, the white appearance was uncommon and was never observed in beating hearts.
FIG. 1. Photomicrographs of capillaries and venules on the surface of the rat heart. For full description, see text. a and b : white appearance of vessels in relaxed, anoxic hearts. C and V denote capillaries and venules. The two large vessels in a are veins. The entire length of a vessel in the focused field can be observed, and the capillary edge is well defined. c-f: red capillaries. c: relaxed anoxic heart. Note that there are few gaps in the erythrocyte columns. Capillary diameter is about the same as in a and b. d: anoxic heart in rigor. Capillaries are narrower than in a-c. Arrows indicate gaps between individual erythrocytes. Note also the long capillary segments which contain no erythrocytes. e and f: beating hearts. Capillaries in e are narrow and gaps in the erythrocyte columns are present; see arrows. Capillaries in fare wider and better filled with erythrocytes. It is likely that e and f were taken in systole and diastole, respectively.
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AND
FIGURE 1. Continued
HONIG
CAPILLARY
DIAMETER
IN
RAT
HEART
263
264
HENQUELL,
LACELLE
FIGURE
AND
HONIG
1. Continued
Figure la illustrates white capillaries (C), venules (V), and two small veins. Some capillaries join others to form a venule which then joins a vein, whereas others join a small vein directly. Note that in the lower right there are two short anastomoses between a capillary and the adjacent vein. Anastomoses are also present between capillaries. Anastomoses are particularly common at the apex of the heart, where they break the capillaries up into rather short segments or loops. Figure 1b illustrates white capillaries at the apex. In general, the diameter of an anastomosis is smaller than that of the capillary from which it arises. Note in Figs. la and lb that the entire length of a capillary in the focused field is discernable. Figure Ic illustrates the appearance of red capillaries in a relaxed, anoxic heart. A clamp was applied to the A-V groove to prevent blood from leaving the capillaries. The capillaries are distended, and the column of erythrocytes within them is nearly continuous. Figure Id illustrates capillaries in an anoxic heart in rigor. The forces acting on the capillaries are analogous to those during systole. No clamp was applied to the A-V groove, so the capillaries were free to empty. Capillary diameter is noticeably smaller than in Figs. la-c. In some places, gaps are present between individual erythrocytes; see arrows. Elsewhere, long capillary segments are empty of erythrocytes. Figure le was obtained in a beating heart. Like the heart in rigor, the capillaries are narrow, with many segments devoid of erythrocytes; see arrows. Figure If was also obtained from a beating heart. Capillary diameter is larger than in d and e but smaller than in a<. As in the relaxed anoxic heart, there are long continuous columns of
265
CAPILLARY DIAMETER IN RAT HEART
erythrocytes with only a few short gaps. It is possible that e and f were taken in systole and diastole, respectively. Mean Capillary Diameter
The mean diameter of white capillaries was slightly larger than red; see Table 1. This might be expected, since measurements of white capillaries include the thickness of the endothelial cells. The difference was only0.2pm, however, and was not statistically significant. Comparison of red and white capillary diameters indicates that measurements on red capillaries are of acceptable precision. All further observations in this paper are based on red capillaries. Note in Table 1 that mean capillary diameter is significantly larger in the beating heart than in the heart in rigor. In contrast, mean capillary diameter in the beating heart is significantly smaller than in the relaxed, anoxic heart. TABLE MEAN
DIAMETER
1
OF SUBEPICARDIAL
CAPILLARIES
Mean diameter Cm)
SD
IN THE RAT
n
Rigor Beating heart
4.12 4.41
1.03 1.10
95 167
Relaxed red capillaries
5.31
1.38
69
Relaxed white capillaries
5.52
1.37
84
P
+---, 10.05 t--l --I
In samples from seven animals, mean capillary diameter was not significantly different in right and left ventricles and in large and small animals (range, 155-520 g). However, observations on a larger population are necessary to exclude a difference on the order of 0.5 pm. Frequency Distributions
Frequency distributions of individual diameter measurements are Gaussian; see Fig. 2. However, the curve for the beating heart (panel C) has a flatter top and fewer observations in its flanks than is expected for the normal distribution. This kurtosis is statistically significant (P < 0.05). The maximum frequency for hearts in rigor (panel A) corresponds to the class 3-4 pm. There are few observations in that class in the distribution for anoxic, relaxed hearts (panel B). The peak frequency in panel B corresponds to the class 5-6 pm. The flat top in panel C contains the classes 3-4 and 5-6 pm, suggesting that it is essentially a composite of panels A and B. The distributions in Fig. 2 are shown as cumulative probability plots in Fig. 3, curves 1,2, and 4. In this form they can be more easily correlated with the properties of erythrocytes.
266
HENQUELL,
Dimensions and Deformability
LACELLE
AND
HONIG
of Erythrocytes
The rat erythrocyte is smaller than that of the human. In suspension its mean volume is 61 pm3, and its mean diameter is 6.8 ,um. Its calculated surface area is 93 rum*. The mean pressure gradient (dP) required to force all cells through a 2.8~pm pipet is only 0.17 mm Hg. As shown in Fig. 4, filled circles, this pressure gradient is less than
CAPILLARY DIAMETER - u
2. Frequencyhistograms of capillarydiameter.A: heartsin rigor: B: redcapillaries in relaxed, anoxichearts;C: beatinghearts.Thedistributionin C hascharacteristics of both A andB. FIG.
1 mm Hg for channels ~2.6 pm. Below 2.5 pm, the requisite pressure gradient rises steeply and linearly from 9.6 mm Hg at 2.45 pm to 104 mm Hg at 1.9 ,um. Mean cell length in the 2.4~pm pipet was 11.2 pm. The channel diameter at which AP rises represents the smallest right cylinder through which a cell can pass without increasing its membrane area. This critical diameter is 2.45 pm for rat erythrocytes. In living microcirculation, the pressuregradient from arteriole to venule is lessthan
10 mm Hg (Smaje et al., 1970). It is therefore useful to know the percentage of erythrocytes which can traverse channels of various diameters when the pressuregradient is restricted to this physiological range. This information is shown by the open circles in Fig. 4. If erythrocyte behavior in uivo is the sameas in vitro, 92% of the cells should
267
CAPILLARY DIAMETER IN RAT HEART
transit 2.5-pm capillaries. It is significant that only 2 % of the capillaries were smaller than 2.5 pm in relaxed hearts (refer to Fig. 3, curve 4). Judging from hearts in rigor (Fig. 3, curve l), about 13 % of subepicardial capillaries are narrower than 2.5 pm during systole. We conclude that all cells can enter all capillaries during diastole and that contraction has little effect on entry of erythrocytes into surface capillaries.
I
2
3
4
CAPILLARY
5
6
DIAMETER
7 -
8
9
IO
u
FIG. 3. Cumulative probability plots of the data shown in Fig. 2. Curve 1: hearts in rigor; curve 2: beating hearts; curve 4: relaxed, anoxic hearts; curve 3: sum of curves 1 and 4.
iii 2 Y E O 1.6 2.0 2.1 2.2 2.3 2.4 2.5 4 MICROPIPETTE
2.6
2.7 2.8
DIAMETER
FIG. 4. The left ordinate indicates negative pressures required to aspirate 100% of the erythrocytes into right-cylindrical glass micropipets whose diameters are shown on the abscissa. Open circles indicate percentage of cells which can be aspirated at pressures less than 10 mm Hg.
The situation within the and Honig, 1964a; Armour mechanical properties of the mural capillary compression
wall is complicated by systolic tissue pressure (Kirk and Randall, 1971). This pressure is opposed by the erythrocytes. The magnitude and consequences of intraare considered below. DISCUSSION
Criticism of Method
Accuracy of capillary diameter measurements is chiefly limited by definition of the capillary edge. In anoxic, arrested hearts, we occasionally observed capillaries with
268
HENQUELL,
LACELLE
AND
HONIG
particular clarity. These white capillary appearances seem to depend on the optical properties of the endothelial cells. We cannot explain what enables us to visualize the capillaries in this way in some experiments but not in others. Nevertheless, the phenomenon is useful because it permits us to identify the limits of the capillary wall very precisely. When we compare diameters of white and red capillaries for the same experimental conditions, no significant difference is observed in mean, variance, or frequency distribution. We conclude from this that the accuracy of our usual measurements on red capillaries is not limited by definition of the capillary edge. The reader should bear in mind that the values we report are means with respect to position along the capillary. Eriksson and Myrhage (1972) report that capillary diameter in living rat skeletal muscle increases by about 1 pm from the arterial to the venous end. Inability to control for this doubtless contributed to the variability we observed. All our measurements were made on longitudinally oriented capillaries. In interpreting them we assume that the capillary cross section is circular. Photomicrographs of capillary casts indicate that this is true of the relaxed heart (Bassingthwaighte et al., 1974). Whether the cross section is circular or eliptical in systole depends on whether compressive forces in the myocardium are uniform in all directions. This appears to be the case for the superficial portion of the wall on which we made our observations (Kirk and Honig, 1964a). The most important limitation of our method is that we can observe capillaries no deeper than 20 pm from the epicardial surface. Although capillary diameter is the same throughout the dead heart (Bassingthwaighte et al., 1974), in the beating heart, compressive forces acting on deep capillaries are considerably greater than those which act on superficial ones (Kirk and Honig, 1964a; Armour et al., 1971). Consequently, our measurements do not apply to systolic capillary diameter deep within the wall. Mean Capillary Diameter under Various Circumstances
The average internal diameter of coronary capillaries postmortem has been measured in silicone-rubber casts. Sobin and Tremer (1972) reported a range of 2-7 pm, with a mean of about 4 pm in various animal species. Bassingthwaighte and co-workers (1974), in a carefully controlled study of canine coronary capillaries, obtained about the same result. They found, however, that procedures used to clear the casts of tissue cause significant shrinkage. When corrected for this artifact, mean capillary diameter was 5.5 pm. They pointed out that high intracapillary pressure and hypoxia during perfusion with silicone-rubber could have increased capillary diameter and suggested that the true value in viva may be less than 5.5 pm. The diameter of coronary capillaries is about the same in the dog and the rat (Sobin, personal communication). Our results can therefore be compared with those of Bassingthwaighte and co-workers. We find mean capillary diameter to be 5.3 pm in anoxic, arrested, relaxed hearts in which capillary pressure is maintained by preventing venous outflow. If measurements on capillaries during rigor, and in relaxed hearts, accurately describe diameters in systole and diastole, the frequency distribution obtained by pooling these measurements should reproduce the distribution obtained for the beating heart. Note in Fig. 3, however, that the pooled data (curve 3) lie to the right of curve 2 (beating heart). In addition, curve 2 does not have a long upper tail. This upper tail could represent capillaries injured by anoxia. If the difference between curves 2 and 3 is
CAPILLARY
DIAMETER
IN RAT
HEART
269
indeed due to anoxic damage, mean capillary diameter in diastole should be about 0.3 pm less than mean diameter in anoxic, relaxed hearts. We conclude that the mean capillary diameter is about 5 pm in diastole. This figure is almost identical to mean capillary diameter in living rat skeletal muscle at rest (Eriksson and Myrhage, 1972). The only measurements of capillary diameter in living heart other than our own are those of Tillmanns et al. (1974). They report diastolic capillary diameter in dog to be 6.3 f 0.08 pm SEM. Their value is probably too large, for it is significantly greater than that of Bassingthwaighte et al. (1974) for maximum capillary diameter in anoxic dog hearts. The overestimate could be accounted for by insufficiently sharp definition of the capillary edge in their tine photomicrographs. Figure 3, curve 4 demonstrates that there are virtually no capillaries less than 2.5 pm in diameter in relaxed, anoxic hearts. It is therefore likely that observations made in diastole do not contribute significantly to the lower tail of the ogive for the beating heart (curve 2). Note also that the lower quartile of the distributions for rigor (curve 1) and for the beating heart are superimposable. On this evidence, mean capillary diameter in systole should be about 4 pm in the superficial regions of the wall. Since systolic tissue pressure is greater than 100 mm Hg in the subendocardium (Kirk and Honig, 1964a; Armour and Randall, 1971), capillaries there should be compressed to the minimum thickness of a rat erythrocyte (about 1.8 pm). We conclude that capillary diameter during systole decreases about 1 pm in the subepicardium and 3 jlrn in the subendocardium. The extent to which capillary segments devoid of erythrocytes narrow during systole is unknown, but if there is free egress of plasma, as implied by observations of Tillmanns et al. (1974), collapse could be complete. Quite recently, actomyosin has been identified in endothelium by means of immunofluorescence (Becker and Nachman, 1973) and thin filaments of actin have been observed attached to the plasmalemma of coronary endothelial cells (Yohro and Burnstock, 1973). It is therefore possible that active changes in capillary diameter occur in addition to passive changes induced by cardiac-muscle contraction. Such changes could be of considerable importance, for they would affect diffusion conditions during diastole. Capillary
Diameter and Erythrocyte
Deformability
The high vo, of myocardium relative to blood flow necessitates a large number of perfused capillaries per volume of tissue. On the other hand, the ratio of capillary blood volume to tissue volume must be small in the interest of efficient contraction. The chief adaptation to these stringencies is small capillaries; 99 ‘A of the capillaries in the beating rat heart are smaller than the mean diameter of an erythrocyte. Erythrocytes can traverse small capillaries because they are highly deformable. The foregoing has been known since Krogh’s description of blood flow in capillaries more than a half a century ago. Nevertheless, our study appears to be the first attempt to quantify the relation between the size and properties of erythrocytes and the dimensions of living capillaries. We find that nature has achieved a perfect match except for complications due to cardiac contraction. All rat erythrocytes can transit a 2.8~pm pipet, and about 92% can transit a 2.5-pm pipet at pressures less than 10 mm Hg. During diastole, almost no capillaries less than 2.5 pm in diameter should exist anywhere in rat myocardium. Systole is equally as long as diastole in the rat. Judging from measurements in dogs (Kirk and Honig, 1964a; Armour and Randall, 1971), peak systolic tissue pressure
270
HENQUELL,
LACELLE
AND
HONKS
greatly exceeds endocapillary pressure, except for the most superficial regions of the wall. Capillary compression is opposed by the mechanical properties of erythrocytes. However, erythrocytes offer little resistance to deformation until capillary diameter reaches 2.5 pm. At that point, the erythrocyte reaches the maximum length attainable without an increase in the area of its membrane. Since compressive forces in tissue increase from 0 at the epicardial surface to more than 100 mm Hg in the subendocardium, a transmural gradient in mean capillary diameter is created by the transmural tissue-pressure gradient. The minimum capillary diameter in the subendocardium should be about 1.8 pm, the minimum thickness of a rat erythrocyte. Capillary compression has two major effects on O2 transport: (1) It hinders entry of erythrocytes into capillaries. As shown in Fig. 4, this hinderance should parallel the transmural gradients in tissue pressure and capillary diameter. Hinderance to entry produces gaps between individual erythrocytes and long capillary segments devoid of erythrocytes. These changes result in regions of tissue in which the extracapillary diffusion path is very long. (2) The 0, content of the capillary per unit length is decreased even where erythrocytes are present, because these latter are deformed into long thin cylinders. Thus, tissue pressure decreases the volume of the 0, source and increases the volume of the sink at the very time r’,, is at a maximum. Calculated pericapillary O2 gradients indicate that the foregoing accounts for the transmural gradient in tissuep0,. Capillary Radius and O2 Gradients
The mean radius of a perfused capillary is about 30% of the mean tissue-cylinder radius in the beating rat heart, but is only 4% of the tissue-cylinder radius in resting rat skeletal muscle (Honig and Bourdeau-Martini, 1973). Because coronary capillaries are so large a fraction of the total diffusion distance their size has a profound effect on 0, transport. An appreciation of the quantitative significance of capillary radius, and of the interaction between capillary radius and capillary spacing, can be gained by use of the Krogh equation; see Fig. 5. In these calculations, Krogh’s 0, diffusion coefficient was used and the po’,, of the rat heart was assumed to be 6.6 x 10m3ml/g/set (BourdeauMartini et al., 1974). The abscissa indicates distance from the center of the capillary. The origin of each isopleth, referenced to the abscissa, indicates the locus of the capillary wall. 2R denotes the center-center distance between capillaries. Each isopleth describes the radial decrement in p0, from the capillary wall for the indicated capillary diameter and spacing. Capillary p02 was set at mean venous p0, in order to simulate conditions at the low end of the longitudinal intracapillary 0, gradient. If this gradient is roughly exponential, the computed tissue O2 gradients approximate conditions in a substantial fraction of the myocardium. Section A illustrates the gradients for normal paOz, coronary blood flow, mean endcapillary pO1, and mean capillary spacing. Note especially that O2 gradients are much steeper for small capillaries. The minimum tissue pOz for a 2-pm capillary is almost 20 mm Hg lower than for an 8-pm one. According to Chance et al. (1973), mitochondrial respiration is not compromised until tissue p0, falls below 0.1 mm Hg. Consequently, even the smallest capiIlaries we observed appear to be sufficient to support aerobic metabolism for these conditions. One of the many limitations of our analysis, however, is that we average PO’,,over the cardiac cycle. If Ijo2 during systole is 50 ‘A greater than average Tioz, some of the tissue supplied by capillaries less than 2.5 pm in diameter
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CAPILLARY DIAMETER IN RAT HEART
would sustain an 0, debt. Only about 15 % of the capillaries are that small in the subepicardium. However, the percentage of capillaries ~2.5 pm should increase progressively with depth and approach 100 % in the subendocardium. Presumably, 0, debts incurred during systole can be repaid during diastole under normal circumstances. The foregoing analysis neglects the fact that large variations in flow velocity (Eriksson and Myrhage, 1972; Tillmanns et al., 1974) and capillary length (Bassingthwaighte et al., 1974) exist. These variations give rise to a frequency distribution of end-capillary
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4
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MICRONSFROM CENTER OF CAPILLARY FIG. 5. Interaction of capillary diameter, capillary spacing, and capillarypOz on calculated gradients of tissuepOz. 2R denotes the center-to-center distance between capillaries. Numerals beside isopleths indicate capillary diameter. See text for description and analysis.
pOZ, with many values less than half of the mean venousp0, (Grunewald and Lubbers, 1975). Gradients in Fig. 5d are computed for the same conditions as in Fig. 5a except that end-capillary pOZ is assumed to be 10 mm Hg. Note that about half of the tissuecylinder cross section would be anoxic even at the mean diameter of subepicardial capillaries. Conversely, no anoxia whatever would exist even around narrow, widely spaced capillaries if capillarypo, were 40-50 mm Hg, as might be the case at the arterial end of the longitudinal 0, gradient. In previous reports we have emphasized that a Gaussian distribution of intercapillary distances exists (Honig and Bourdeau-Martini, 1973; Bourdeau-Martini et al., 1974). Figure 5c illustrates gradients around widely spaced capillaries; all other conditions are as in a. Even if vo, is averaged over the cardiaccycle, some of the tissue supplied by capillaries less than 3 pm in diameter would be anoxic. The amount of anoxic tissue depends on the frequency distributions of critical parameters. In the normal rat heart only about 20 % of the superficial capillaries are spaced as widely as in Fig. 5c and only about 25 ‘A of the subepicardial capillaries are narrower than 3 pm. The frequency dis-
272
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tribution of end-capillary pOZ is not presently available. Obviously, hypoxia should be much more extensive in the subendocardium, where during systole the frequency distribution of capillary diameter should be shifted to the left, and that of intercapillary distance to the right. Figure 5b illustrates conditions in moderate hypoxia. lioZ is the same as in a, but the mean intercapillary distance is assumed to be 3 pm shorter. Such a decrease in intercapillary distance has actually been observed in the living heart (Honig and BourdeauMartini, 1973; Bourdeau-Martini et al., 1974). Tissue 0, gradients are not as steep as in a and c because the capillaries are more closely spaced. ~0, at the capillary wall is so low, however, thatp0, goes to 0 in portions of the tissue supplied by capillaries less than 3.5 pm in diameter. From Fig. 3, we estimate that about 50 % of the subepicardial capillaries are less than 3.5 pm in diameter during systole, whereas only about 20 % are less than 3.5 ,um during diastole. We conclude that under hypoxic conditions the decrease in capillary diameter during systole has important consequences for 0, transport. Note that the small size of coronary capillaries limits the effectiveness of capillary recruitment in compensating for hypoxia: If all capillaries were 4 pm wide, aerobic respiration would be possible throughout. Recruitment is nonetheless essential. Figure 5d illustrates the effect of hypoxia if recruitment were impaired, as, for example, in hypertrophy (manuscript in preparation). Conditions are the same as in Fig. 5b except that 2R is 3 ym larger. Anoxia would exist in some of the tissue supplied by capillaries smaller than about 6 ym. This includes about 90 % of the capillaries in the myocardium, even in diastole. In recent years, highly sophisticated models of 0, transport have been developed based on iterative computing techniques (Grunewald, 1973). The magnitude of the interaction of diffusion distance and capillary diameter indicates that the frequency distributions of both parameters, and fluctuations in the distributions during the cardiac cycle, must be included in such models.
The Transmural Gradient in Tissue pO1 By use of 0, electrodes, ~0, in the subendocardium has been found to be about half of that in the subepicardium (Kirk and Honig, 1964b; Moss, 1968; Winbury et al., 1971; Whalen et al., 1973). A corresponding transmural gradient in the ratio of NAD+ to NADH has been measured by direct chemical assay (Hayashi et al., 1974). The following explanations for the transmural O2 gradient have been offered: (1) diffusional shunting (Bassingthwaighte et al., 1974); (2) low subendocardial blood flow (Kirk and Honig, 1964b); and (3) high subendocardial vo’,, (Winbury et aE., 1971). 1. Judging from the behavior of tritiated water, a significant diffusional shunt at the level of the capillaries is unlikely at normal coronary flow (Yipintsoi and Bassingthwaighte, 1970). This is in accord with the fact that coronary capillaries are almost exclusively concurrent (Tillmanns et al., 1974). However, Bassingthwaighte et al. (1974) point out that the arrangement of conducting vessels is consistent with 0, diffusion from arteries to veins. Though more experiments to this point are required, no evidence of a diffusional shunt for 0, could be obtained in isolated rat hearts (Huhmann et al., 1967). 2. Early studies based on depot clearance revealed an apparent transmural gradient in coronary flow (Kirk and Honig, 1964b). Though average subendocardial
273
CAPILLARY DIAMETER IN RAT HEART
flow may indeed be low in certain disease states (Kjekshus, 1973), evidence based on microspheres indicates that the ratio of epicardial to endocardial flow is close to unity in the normal heart (Domenech et al., 1969; Kjekshus, 1973). 3. When a coronary artery is occluded, tissue pOz estimated with 0, cathodes falls most rapidly in the subendocardium, suggesting that tie, is greatest in this region (Winbury et al., 1971). However, several other interpretations are possible, and high ro, in the subendocardium is inconsistent with the fact that longitudinal tension in endocardial muscle fibers is about a third less than in epicardial fibers (Armour and Randall, 1971). Even if vo, were greater in the subendocardium, the effect of this on tissue ~0, should be compensated by the short diastolic diffusion distances characteristic of this region (Myers and Honig, 1964). We conclude that none of the foregoing explanations is satisfactory. Figures Id and le demonstrate that contraction excludes erythrocytes from long segments of coronary capillaries. Since the 0, capacity of an empty capillary is negligible, the distance between functional capillary segments increases during systole. The locus of a collapsed capillary segment is random and therefore different from beat to beat. The diameters of capillaries which contain erythrocytes are determined by the relationship between tissue pressure and erythrocyte deformability; refer to Fig. 4. These effects of contraction increase from the epicardium to the endocardium, in parallel with the tissue-pressure gradient. Consequently, the volume of tissue which a capillary can service is decreased at the very time when blood flow is lowest, voz is highest, and regions of long intercapillary distance exist. As shown in Fig. 5, this combination of conditions should produce anoxia in a substantial portion of the tissue. In agreement with this prediction, Whalen and co-workers (1973) reported that in cat hearts, ~0, was between 0 and 5 mm Hg in 27 % of the subepicardial cells and in 61% of the cells more deeply situated. We conclude that the transmural gradient in tissue pOz is best explained by the effect of tissue pressure on the dynamics of the coronary capillary circulation. ACKNOWLEDGMENTS We thank Mr. William H. DeVeer for help with the photography. Mr. James L. Frierson provided expert technical assistance. This research was supported by Grants HL-03290, HL-16421, and HL-18208 from the National Institutes of Health and by a grant-in-aid from the Genesee Valley Heart Association. REFERENCES 1.
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