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The distensibility of single capillaries and venules in the cat mesentery
MICROVASCULAR RESEARCH 20, 358-370 (1980)
The Distensibility of Single Capillaries and Venules in the Cat Mesentery L . H . SMAJE, 1 P. A . FRASER, 2 AND GERALDINE CLOUGH a
Department of Physiology, University College London, Gower Street, London WCIE 6BT Received November 1, 1979 The distensibility of single capillaries and venules of the cat mesentery has been determined using a simple technique in vivo. Selected vessels were occluded under microscopic control and red cell oscillation in the occluded segment was monitored using cinemicrography. The cells were seen to oscillate in synchrony with local vascular pressure which was recorded simultaneously using the servo-null technique. Less than 10% of the oscillation could be accounted for by filtration/reabsorption so the bulk of the movement was thought to be a consequence of distension of the vessel during systole and relaxation during diastole. Changes in radius would be amplified by the factor 2Ur (where r is radius and ~ the length of the occluded vessel) to give the observed movement of red cells. Mean pulse pressure was 3.2 mm Hg in capillaries and 2.3 mm Hg in venules which gave rise to increases in radius of 0.03 and 0.028/zm, respectively. The nature of the structure supporting the vessels was considered and it seemed likely to be the basement membrane which would require a Young's modulus of 1.8 × 106 N m-2 for the capillary and 5.4 × 106 N m-2 for the venule although pericytes might contribute to support of the latter. It is considered likely that some of the higher values quoted in the literature are due to measurements being made at different ends of a nonlinear stress-strain curve, the present data being obtained at the low stresses normally found in mammalian microvessels.
INTRODUCTION
Capillaries are generally thought to be indistensible since increases in transmural pressures of 50 mm Hg (7 kPa) or more produce no observable change in diameter (Baez et al. 1960). Two explanations have been offered to explain this rigidity. One hypothesis views the capillary as a "tube-in-liquid": the capillary walls themselves bear the distending stress because, as a result of their small diameter, the tangential wall tension is very low (Burton, 1954). The alternative point of view, proposed by Fung et al. (1966), considers the capillaries as a "tunnel-in-gel": here support for the capillary is provided by the surrounding gel. The tube-in-liquid hypothesis was criticized on the grounds that the endothelial cell wall and basement membrane would have to have a Young's modulus similar i Present address: Department of Physiology, Charing Cross Hospital Medical School, Fulham Palace Road, London W6 8RF. 2 Present address: Department of Physiology, King's College, Strand, London WC2R 2LS. 3 Medical Research Council Scholar. Present address: University Laboratory of Physiology, South Parks Road, Oxford OXI 3PT. 358 0026-2862/80/060358-13502.00/0 Copyright © 1980by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in U.S.A.
M1CROVASCULAR DISTENSIBILITY
359
to that of collagen. Although Fung et al. (1966) performed some elegant experiments on pieces of mesentery and provided a sophisticated analysis of the data at their disposal, they had no information on the actual distensibility of the capillaries. Instead they accepted the observations of Baez et al. (1960) but assumed an upper limit of distension based on the optical resolution available to Baez et al. A more refined method of measuring capillary distensibility was introduced by Clough et al. (1974), who, on the basis of their measurements, put forward the view that the capillary basement membrane, which contains type IV collagen (Kefalides, 1980), does provide the necessary support. Murphy and Johnson (1975), in a brief review, came to a similar conclusion. More recently, in direct contrast to the findings of Baez et al. (1960), Bouskela and Wiederhielm (1979) showed in a preliminary communication that the diameters of capillaries do increase in response to increases in transmural pressure. Furthermore they calculated that this distensibility is consistent with the basement membrane bearing the stress. In this paper we describe experiments in which the distensibilities of capillaries and venules have been measured by analyzing the oscillations of red cells in microvessels occluded with a small glass needle. From these results we have been able to make estimates of the Young's modulus of elasticity of the vessel walls. METHODS Animals and anesthesia. Experiments were performed on the mesentery of cats of either sex weighing between 1.2 and 2.5 kg. Anesthesia was induced by ethyl chloride and maintained by ether until pentobarbitone (up to 35 mg/kg) could be given via a cannula placed in the femoral vein. Supplementary doses (0.5 ml, 12 mg/ml) were given as required. The trachea and femoral vessels were cannulated routinely. Blood pressure was measured in the abdominal aorta via a Portex (Hythe, Kent) nylon I.V. cannula connected to a pressure transducer (Bell & Howell Type 4-326-L212) and registered on a Devices M4 pen recorder. The cannula and transducer were filled with 0.9% NaCI containing l0 IU heparin/ml. The temperature was maintained at 37° using a heating blanket placed beneath the cat, controlled via a rectal thermistor using the circuit described by Diete-Spiffet al. (1962). Preparation ofmesentery. A longitudinal incision 2-3 cm long was made in the shaved skin over the umbilicus and the animal was laid on its side on a Perspex tray which had a heated side chamber to take the mesenteric preparation. A loop of colon was drawn out of the incision using cotton-wool buds soaked in Krebs solution and its mesentery was placed over a glass-topped pillar in the side chamber positioned above the microscope substage condenser. The intestine rested on cotton-wool soaked in Krebs solution placed around the base of the pillar, and the whole of the exposed tissue was then covered in plastic film (Snappies Cling Film Wrap, Empress Products Ltd.) except for the region of the mesentery under investigation which was irrigated with the Krebs solution. This was composed as follows: NaCI, 118 mM; KCI, 4.7 mM; CaCI2, 2.5 mM; KH2PO4, 1. i mM; MgSO4-7H20, 1.25 mM; NaHCO~, 25 mM; glucose, 11 mM; bubbled with
360
SMAJE, FRASER, AND CLOUGH
95% 02, 5% CO2, and heated to 37° in the final conduit by a stainless-steel heater. This was heated by a resistance wire and controlled by an incorporated thermistor using the circuit of Diete-Spiff et al. (1962), and further checked by a thermistor cemented to the stage beneath the mesentery. The mesentery was irrigated at 4 ml/min using a roller pump and the tube was positioned using a small micromanipulator attached to the animal tray. Microscopy and filming. The tray containing the cat was clamped to a modified stage of a Leitz lntravital microscope equipped with standard Orthoplan optics. The tissue was transilluminated with a Leitz high-pressure 150-W xenon lamp using neutral density filters to adjust the amount of light and a green filter to enhance the contrast of the red cells and to provide monochromatic light for photography. A long-working distance condenser (22 mm) and long-working distance objectives (UM series) were used. The image was split so that light passed through to a binocular viewing head and to an Arriflex H16 16-mm cine camera mounted vertically above the microscope, llford Pan F film was used at 25 frames/sec. Vessels were occluded by glass probes (Micropipettes fused at the tip), held in a Leitz micromanipulator. The probes were pulled from Leitz Pyrex tubing (o.d., 1.2 mm) to give a flexible shank about 15-20/~m in diameter and the tips were fused in a small gas flame to provide a ball 10-50 tzm in diameter. Pressure was measured in the selected vessel by insertion of sharpened glass micropipettes attached to a resistance null-balance servo system of the type described by Wiederhielm et al. (1964) and modified by lntaglietta et al. (1970). Film exposure was determined using a Leitz Microsix exposure meter. Exposed film was developed commercially (Humphrey's Laboratories Ltd.) and frame-byframe analysis undertaken using a PCD XY data reader fitted with a Vanguard 16-mm motion analyzer cine head. Microscope magnification was 160 and the final magnification on the analyzer screen × 1000. The output from the data reader was digitized by a Farnell DCV 100 voltmeter and fed via an 8-channel interface to a Data Dynamics Model 390 teletype and paper tape punch. Vessel radius was measured on the film analyzer. In most experiments a xenon light source was used but in some, red cell position was determined exactly with respect to time by using a stroboscopic light source synchronized to the camera with a simultaneous write out of the pulses on the pen recorder (Clough, 1977). RESULTS Occlusion of the venous end of a capillary leads to movement of the red cells toward the occluding probe. The movement is not smooth but oscillatory, synchronous with the changes in pressure in the supplying arteriole (Fig. 1). Red cells continue to pack down until the plasma colloid osmotic pressure, increased by ultrafiltration, balances the hydrostatic pressure tending to produce filtration. It is important to note that red cell oscillation continues after net movement ceases. This oscillation could be a consequence of either alternate filtration and reabsorption or of distension of the capillary walls during systole and relaxation during diastaole. These alternatives will be examined in turn.
361
MICROVASCULAR DISTENSIBILITY
E
o
2 8 O 2 6 0" 2 4 0
°, . . . .
o
220
200
i
i
1
2 Time
3
Seconds
FI6. I. Oscillatory motion of red cells following occlusion of a single capillary. Dots show individual measurements of column length obtained by frame-by-frame analysis of cine film. The solid line is a fitted monoexponential.
(i) A l t e r n a t e filtration a n d reabsorption
The rate of filtration may be calculated from the equation
Q Jv -
A
- Lp (Pc - IIc),
(1)
where Jv is fluid flux, Q is flow rate, A is exchange area, Lp is filtration coefficient, Pe is capillary hydrostatic pressure, and lie is plasma colloid osmotic pressure. When net red cell m o v e m e n t ceases, mean hydrostatic pressure, Pro, equals II c (see Fraser et al. 1978). The oscillation would then be accounted for by the pulse pressure, AP, where AP = Pc - Pro. Assuming a sinusoidal wave form, fluid m o v e m e n t would thus be L p A P sin tot
Jv -
(2)
2
Red cells in capillaries and venules are good markers of fluid m o v e m e n t (Fraser et al. 1978, and see Discussion) so the oscillatory motion of the red cell due to filtration may be found from J,, A
=
7rr~
d(
Lp A P sin cot
2~r(
dt
2
'
(3)
assuming that the magnitude of oscillation has an insignificant effect on Hc (see Discussion), and, where r is radius of vessel, t ~is length of occluded segment. The distance m o v e d by the red cell (Ag') as a consequence of filtration will be At" = - r
• Lp Ap[ t=Tr sin oJt dt. )t=O
(4)
362
SMAJE, FRASER, AND CLOUGH
This can be shown to be (~Lp AP A(' -
7rrf
'
(5)
where f is pulse frequency. The geometry of the occluded vessel is simply measured and Lp a n d f are obtained by analysis of the occlusion data, Mean red cell movement reflects fluid movement so the mean rate of red cell packing may be used to calculate fluid flux (see Fraser et al. 1978 and Discussion). Initial plasma colloid osmotic pressure is obtained using a plasma sample and Pe is measured by direct puncture. Hydrostatic and colloid osmotic pressures in the interstitium are not taken into account as the values are relatively small (see Clough and Smaje, 1978) and are unlikely to fluctuate with the pulse. Red cell packing rate can be closely approximated by a monoexponential (see Fraser et al. 1978) which was fitted to the data as shown in Fig. 1. The oscillatory component of red cell movement was then extracted by subtracting the exponential curve from the raw data. The frequency of oscillation was obtained simply by measuring the time taken for 6-10 cycles, and the mean change in red cell position A~¢ by averaging the extreme positions in the same cycles. The observed red cell movement, A(, can now be compared with that predicted on the basis of filtration (AC) using the values obtained following occlusion. Table 1 lists these data for both capillaries and venules and it can be seen that the calculated movement, AC, is about 4 and 10%, respectively, of the observed movement, A(. There was no significant difference in A( when determined near the beginning of an occlusion or toward the end when net red cell movement was minimal. Hence alternate filtration-reabsorption cannot be responsible for the major part of red cell oscillation following occlusion.
(ii) M i c r o v e s s e l D i s t e n s i o n
The most likely alternative explanation is distension of the vessel during systole and recoil in diastole. The geometry is simple, as seen in Fig. 2. Ignoring second-order terms, it is assumed that the volume occupied by the changed red cell position, A~Trr2, is accompanied by a slight expansion of the radius of the occluded vessel, Ar and this volume will be 27rrAr~. Equating these gives Ar -
rA~ 2~
(6)
The change in radius is thus amplified by the factor 2(/r. Assuming a minimum resolution for A( of about I txm and a typical capillary length of 100-200/~m, this allows measurement of a change in radius of 0.01 /zm or less, well below the resolution of the light microscope. The mean values for the change in radius in capillaries and venules in the present experiments were 0.030 and 0.028 tzm as seen in Table 1. It is now possible to calculate compliance of the vessel wall. If the vessel is considered to be a tube in liquid and the wall as a whole is withstanding the applied
363
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364
SMAJE, FRASER, A N D CLOUGH
I
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FIG. 2. Diagrammatic representation of changes in geometry of the occluded vessel with changes in hydrostatic pressure.
pressure, then the incremental Young's modulus Ein c of the wall can be determined from E = A stress/A strain. By using the Laplace relationship (P = T/r): Einc =
A stress A strain
APr
1
=
APr 2
1
- -
Ar/r
x
°
Ar
_
_
x
,
(7)
where x is thickness of supporting structure in the wall. Values of Ein~C (Young's modulus × wall thickness) are listed in Column l0 of Table I. Ein~X is a composite value making no assumptions about the structure(s) supporting the wall except that the support is coming from the wall itself rather than the surroundings. Laplace's law obviously only approximates to the situation and the walls cannot be considered to be thin relative to the diameter. The value for Einc may be calculated using a formulation for thick-walled tubes (Love, 1927) as follows: AP Ein e = ~
Ar
2(1 - o"z) rl 2 (rl + x) (rl + x)~ - rl 2
,
(8)
where rl is internal radius and ~ is Poisson's ratio, assumed to be 0.5. The values calculated using L o v e ' s equation differ somewhat from the simple application of Laplace's law but are of a similar order of magnitude. Table 2 shows values calculated for Ein~ using the mean data obtained from Table I and Eq. (8) and assuming that support for the vessel is coming from the layer of the wall specified in Table 2. The alternative "tunnel in gel" hypothesis may be approximated by considering the mesentery to be a thick tube surrounding the vessel whose inside radius is the measured value and whose wall thickness x is (z - r)/2, where z is the mesentery thickness. Using Eq. (8) and a mesentery thickness of 70/~m, Eine for capillaries and venules is 1.04 × l04 and 3.22 x l04 N m -2, respectively. DISCUSSION The present results need to be compared with data derived from the perfusion experiments of Baez et al. (1960) and from the calculations of compliance based
MICROVASCULAR
365
DISTENSIBILITY
TABLE 2 CALCULATIONS FOR YOUNG'S MODULUS FOR STRUCTURES OF THE VESSEL WALL BASED ON THE ASSUMPTION THAT THE STRUCTURE CONCERNED ALONE PROVIDES SUPPORT
Capillaries
Whole wall Endothelium Basement membrane Whole mesentery
Venules
X
Ein e
X
Etn e
~m)
(N m-~)
~m)
(N m-2)
1.5 0.4
3.88 × 1@ 1.4 x 106
0.1
5.4
0.5 0.3
3.7
0.1
1.8
31
× 1@ 6.1@ x 106
1.04 x 104
27
x 106
3.22 x 104
Note. A p p r o p r i a t e m e a n v a l u e s f r o m T a b l e 1 t o g e t h e r w i t h v a l u e s of t h i c k n e s s f r o m the l i t e r a t u r e are u s e d for s u b s t i t u t i o n into Eq. (8).
on measurements of pulse velocity in the microcirculation undertaken by Intaglietta et al. (1971). However, the validity of the present measurements will be assessed before they are interpreted in relation to theories attempting to account for microvascular rigidity and the known structure of the capillary and venular walls. Validity o f the Present Measurements
We have a method of measuring capillary and venular distensibility which is critically dependent on the assumption that the movement of red cells accurately reflects the motion of the plasma. This problem has been considered previously (Fraser et al., 1978) and it was established that the net cell motion did indeed reflect the transendothelial fluid flux. All the vessels studied had larger diameters than red cells (i.e., positive clearance) so that the situation in which lubrication theory (Fitz-Gerald, 1969) must be considered, does not apply. In addition platelets were observed, on occasion, within the occluded capillary segments, and they moved with the red cells. However, velocity at the wall must be zero and thus red cell velocity will overestimate mean plasma flow to some extent. Even in freely flowing capillaries red cell velocity is only 1.3 times that of mean velocity (Gaehtgens et al., 1976; Lipowsky and Zweifach, 1978) and the undistorted shape of red cells in the present situation means that the overestimate will be even less and the measurements of Einc underestimated in proportion. The curve for red cell column length vs time is fitted well by a monoexponential in many capillaries (e.g., Fig. 1) but it is a less satisfactory fit for very permeable vessels and those in which there is a very small equilibrium relative cell separation (¢0/¢oo <0.8). In applying the technique generally, therefore, difficulties could arise with some vessels. Although no conscious selection occurred in the present experiments, it should be pointed out that the present values for Lp are lower than those obtained in a previous study in the cat mesentery (Fraser et al., 1978). It is likely that this
366
SMAJE, FRASER, AND CLOUGH
represents a sampling problem. If the previous Lp values are taken to be representative of the microvasculature as a whole, then filtration/reabsorption accounts for a somewhat larger proportion of red cell movement than calculated here. The proportions increase from 4 and 10% in capillaries and venules, respectively, to 10 and 12%. This still indicates that filtration/reabsorption makes a minor contribution to red cell oscillation and does not affect our main conclusions. A further assumption in our analyses is that IIc does not change significantly during individual red cell oscillations (Eq. (4)). The relationship Lp AP/Ilrf gives the proportionate increase in protein concentration during the half cycle. This gives a fractional increase of 0.0014 and even assuming a protein concentration of 10% at equilibrium, an unlikely high value, such an increase in concentration does not lead to a significant increase in IIc and our assumption is seen to be valid.
Rigidity of the Microvascular Wall If we begin by assuming that the capillary wall, or some part of the wall, provides the necessary support then Young's modulus may be obtained by dividing the values for Ein~X in column 10 of Table 1 by the thickness of the layer concerned, x, or more accurately by using Love's formula (Eq. (8) vs). There seems to be some doubt about the thickness of the basement membrane as quoted values vary from 0.02 to 0.18/~m but a reasonable value for the present purposes would be 0. I/~m (Williamson et al. 1969). No data are available for the thickness of venular basement membrane but they are assumed to be the same as those for capillaries. This value, together with those obtained by Rhodin (1968) for capillary and venular dimensions of the whole vessel and of its endothelium are used in Table 2 for calculations of Young's modulus using Love's equation. It can be seen that Young's modulus for capillaries and venules are similar if the whole wall is considered the supporting structure, but if support comes from the endothelium or basement membrane alone or is provided by the interstitium, different values are found for the two types of vessel. This aspect of the study will be considered later, but meanwhile a comparison of the present values with data in the literature is of interest. From Table I it is seen that the mean change in capillary radius was 0.03/~m for an increase in hydrostatic pressure of 3.36 mm Hg. On this basis, an increase in diameter of 1.8 p.m would have been expected for the transmural pressure increase of 60 mm Hg employed by Baez et al. (1960) whereas no increase was detected. The most likely explanation for this apparent discrepancy is that capillaries have a nonlinear stress-strain relationship, the stress increasing disproportionately at higher strains. This was observed with arterioles (Wiederhielm, 1965) and capillaries (Bouskela and Wiederhielm, 1979). With increasing distension, arteriolar walls become stiffer, Young's modulus for the wall varying from about I x 105 N m-2 at 5% above normal strain to about 45 × l0 s N m -2 at 30% above normal strain. Similarly, reducing pressure below 15 mm Hg led to a fall in vessel diameter in the experiments of Baez et al. (1960) but these authors attributed this to critical closure of the vessels. Unfortunately, insufficient points on the pressure-diameter relationship were obtained to be sure of the interpretation. However, a range of pressure-diameter values is available for renal tubule and
367
MICROVASCULAR D I S T E N S I B I L I T Y
isolated renal tubule basement membrane. Young's modulus varies from about 3.3 x 10n N m -2 at pressures between 10and 30 mm Hg to 5.7 x 106 N m -2 for pressures between 30 and 60 mm Hg for both intact tubule and for isolated basement membrane (calculated from Welling and Grantham, 1972). Collagen is well known to show stiffening at higher strains (Burton, 1954) and it seems reasonable to conclude that collagen in the basement membrane or elsewhere in the microvessel wall may well be responsible for the nonlinear stress-strain relationship of such vessels. However, Fung et al. (1966) also found marked nonlinearity for rabbit mesentery but this tissue too contains collagen (about 15% according to Fung et al.). As can be seen in Table 3, the absolute magnitude of the Young's modulus obtained for the whole wall in the present experiments is comparable with those obtained for arterioles at low strains but less than that suggested by Fung et al. (1966) on the basis of their analysis of their own data and that of Baez et al. (i 960). It is more difficult to reconcile our findings with those of lntaglietta et al. (1971), who calculated a much lower Young's modulus. They explained the high compliance value they calculated from pressure pulse velocity across the microcirculation as being chiefly due to the distorting effect of red cell oscillation caused by filtration-absorption. We have shown from our measurements of pressure and filtration coefficients, however, that filtrationreabsorption can account for merely 4-10% of the oscillation (Table 1). If filtration-reabsorption were the explanation, backward movement of the red cells during an occlusion would occur only if diastolic pressure decreased below plasma colloid osmotic pressure. The available evidence suggests that this does not
TABLE 3 VALUES FOR YOUNG'S MODULES OF CERTAIN TISSUES FOR COMPARISON WITH PRESENT VALUES Young's modulus (N m 2) Structure Cat mesenteric capillaries (a) Whole wall (b) Basement membrane Cat omental capillaries Whole wall Frog mesenteric arterioles Whole wall Whole mesentery Renal tubule basement membrane Lens capsule basement membrane Collagen
Authors
Low strain
High strain
Present 3.7 x 10~ 1.8 × 10~ lntaglietta et al. 1971 (Recalculated)
Wiederhielm, 1965 Fung et al., 1966 Welling and Grantham, 1972 Fisher and Wakely, 1976 Bergel, 1961
1.5 x 1@
1.2 × 1@ 0.9 x l(P
4.5 x 106 1.8 x 106
3.3 × 10~
5.7 × 106
0.8 x l0n 1 × 107
7.7 x l0 n lxl0 ~
368
SMAJE, FRASER, AND CLOUGH
happen in freely flowing vessels in the mesentery (Zweifach, 1964; Fraser et al. 1978). Since filtration/reabsorption can account for only about 10% of red cell oscillation, the very high compliance found by lntaglietta et al. (1971) needs to be explained. Their value for Young's modulus, 4.5 × 104 N m-2 for the whole wall is certainly less than the usually quoted values but it was obtained at normal pressures and should thus be compared with our value of 3.7 × 1@ N m-2. In their calculations they used a ratio of radius:wall thickness of l:9 based on the measurements of Baez (1969). These do not accord with electron microscopical measurements (Rhodin, 1968; Simionescu et al. 1975) and a ratio of about 10 would appear more appropriate. If this value is used the Young's modulus becomes 1.5 × 105 N m -2, which completely alters the interpretation of their data and is remarkably close to the present value. It should be noted that our calculations assume isotropy and no change in vessel length. No changes were observed so the assumption seems reasonable.
Structure Responsible f o r Support
Endothelial cells are generally thought to have little resistance to deformation (see Fung et al. 1966) and are unlikely to provide the necessary support. Certainly the presence of renal tubular epithelial cells makes no difference to the distensibility of renal tubules, the support for which comes from their basement membrane (Welling and Grantham, 1972). If basement membrane were responsible in capillaries as well, it would require a Young's modulus of i.8 × 1@ N m-z, which is similar to the value found for renal tubule and lens capsule basement membranes (Fisher and Wakely, 1976; see Table 3). These values are below the range quoted for collagen (3-100 x 106 N m-Z; Bergel, 1961) but if the basement membrane were thinner than the value used for the present calculations, as is possible, then our values would fall within the lower end of the range. Fisher and Wakely (1976) found that lens capsule basement membrane had a lower Young's modulus than collagen but calculated that the filaments from which the basement membrane and collagen were formed had the same elastic moduli. The difference in measured Young's moduli was explained partly by filament arrangement and partly by differences in the angle of tilt of the helices of individual filaments while the nonlinear stress-strain relationship was thought to be a consequence of the uncoiling of the helices. Williamson et al. (1969) made the interesting observation that capillary basement membrane thickness is correlated with transmural hydrostatic pressure which suggests that basement membrane has an important role in the support of capillaries. The higher value for EineX in venules could be accounted for if the basement membrane were thicker in these vessels, although there is no information on this point, or it could be due to the presence of the pericytes and the tethering effects of their associated collagen fibrils (see Rhodin, 1968). While the overall value for vessel distensibility found here could certainly be provided by support from the surrounding gel, the larger diameter of venules would predict a greater distensibility and a similar Young's modulus, whereas we found venules to have a greater Young's modulus. Furthermore, if the interstitium did provide support, our somewhat simple calculations suggest that the Young's
MICROVASCULAR DISTENSIBILITY
369
modulus determined by Fung et al. (1966) is too high. However, the detailed arrangement of collagen within the mesentery is not known and, as pointed out by Fung et al. (1966), it is necessary to know the detailed structure of complex tissues before their mechanical characteristics can be computed. The present experiments thus provide a technique for measuring distensibility in single capillaries and venules and tend to suggest that the basement membrane and pericytes are responsible for support. Our calculations also suggest that the microvessels are normally acting at a low point in their stress-strain relationship and that the high values often quoted are a consequence of measurements taken at higher parts of the nonlinear stress-strain relationship. APPENDIX 1: LIST OF SYMBOLS
JV
Q
A Lo Pc Pm AP Hc r Ar rl
t At At'
f o) x (7.
t z
Einc
rate of volume flux rate of fluid flow out of occluded segment surface area filtration coefficient capillary hydrostatic pressure mean capillary hydrostatic pressure pulse pressure plasma colloid osmotic pressure vessel radius change in radius internal radius length of occluded segment red cell oscillation distance moved by red cell as a consequence of filtration pulse frequency angular velocity thickness of supporting structure in wall Poisson's ratio time thickness of mesentery incremental Young's modulus ACKNOWLEDGMENTS
The British Heart Foundation is gratefully acknowledged for a project grant to L. H. S. We are most grateful to Mr. S. R. Rawlinson for his expert technical assistance and to Dr. D. H. Bergel for his helpful criticism of the manuscript.
REFERENCES BAEZ, S. (1969). Simultaneous measurements of radii and wall thickness of microvessels in the anesthetized rat. Circ. Res. 25, 315-329. BAEZ, S., LAMPORT, H., AND BAEZ, A. (1960). Pressure effects in living microscopic vessels. In "Flow Properties of Blood," pp. 122-136. A. L. Copley, and G. Stainsby, eds., Pergamon, London. BERCEL, D. H. (1961). The static elastic properties of the arterial wall. J. Physiol. 156, 445-457. BOUSKELA, E., AND WmDERmELM, C. A. (1979). Viscoelastic properties of capillaries. Microvasc. Res. 17, SI.
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BURTON, A. C. (1954). Relation of structure to function of the tissues of the wall of blood vessels. Physiol. Rev. 34, 619-642. CLOUGH, G. F. (1977). The Influence of the lnterstitium on the Mechanical and Transport Properties of the Mesenteric Microvasculature. Ph.D. Thesis, London. CLOUGH, G., FRASER, P. A., AND SMAJE, L. H. (1974). Compliance measurement in single capillaries of the cat mesentery. J. Physiol. 240, 9P. CLOUGH, G. AND SMAJE, L. H. (1978). Simultaneous measurement of pressure in the interstitium and the terminal lymphatics of the cat mesentery. J. Physiol. 283, 457-468. DIETE-SPIFF, K., IKESON, C., AND READ, G. L. (1962). Constant temperature device for use with biological microscopes. J. Physiol. 162, 44-45P. FISHER, R. F., AND WAKELY, J. (1976). The elastic constants and ultrastructural organization of a basement membrane (lens capsule). Proc. Roy. Soc. London B, 193, 335-358. FITZ-GERALD, J. M. (1969). Implications of a theory of erythrocyte motion in narrow capillaries. J. Appl. Physiol. 27, 912-918. FRASER, P. A., SMAJE, L. H., AND VERmNDER, A. (1978). Microvascular pressures and filtration coefficients in the cat mesentery. J. Physiol. 283, 439-456. FUNG, Y. C., ZWEIEACH, B. W., AND INTAGLIETTA, M. (1966). Elastic environment of the capillary bed. Circ. Res. 19, 441-461. GAEHTGENS, P., BENNER, K. U., SCHICKENDANTZ, S., AND ALBRECHT, K. H. (1976). Method for simultaneious determination of red cell and plasma flow velocity in vitro and in vivo. Pfl/igers Arch. 361, 191-195. INTAGLIETTA, M., PAWULA, R. F., AND TOMPKINS, W. R. (1970). Pressure measurements in the mammalian microvasculature. Mierovasc. Res. 2, 212-220. INTAGLIETTA, M., RICHARDSON, D. R., AND TOMPKINS, W. R. (1971). Blood pressure, flow, and elastic properties in microvessels of cat omentum. Amer. J. Physiol. 221 (3), 922-928. KEEALIDES, N. A. (1980). Chemistry of basement membranes: structure and biosynthesis. In "Advances in Microcirculation,'" Vol. 9, pp. 295-322, Karger, Basel. LIPOWSKV, H. H., AND ZWEIFACH, B. W. (1978). Application of the "'two-slit" photometric technique to the measurement of microvascular volumetric flow rates. Microvas. Res 15, 93-101. LOVE, A. E. H. (1927). "'A Treatise on Mathematical Elasticity," 3rd Ed., Cambridge Univ. Press, London/New York. MURPHY, M. E., AND JOHNSON, P. C. (1975). Possible contribution of basement membrane to the structural rigidity of blood capillaries. Microvasc. Res. 9, 242-245. RHODIN, J. A. (1968). Ultrastructure of mammalin venous capillaries, venules, and small collecting veins. J. Ultrastruct. Res. 25, 452-500. SIMIONESCU, M., SIMIONESCU, N., AND PALADE, G. E. (1975). Segmental differentiations of cell junctions in the vascular endothelium. J. Cell Biol. 67, 863-885. WELLING, L. W., AND GRANTHAM, J. J. (1972). Physical properties of isolated peffused renal tubules and tubular basement membranes. J. Clin. Invest. 51, 1063-1075. WIEDERHIELM, C. A. (1965). Distensibility characteristics of small blood vessels. Fed. Proc. 24, 1075-1084. WIEDERmELM, C. A., WOOOBURY, J. W., KIRK, S., AND RUSHMER, R. F. (1964). Pulsatile pressures in the microcirculation of the frog's mesentery. Amer. J. Physiol. 207, 173-176. WILLIAMSON, J. R., VOGLER, N. J., AND KILO, C. (1969). Estimation of vascular basement membrane thickness. Diabetes 18, 567-578. ZWEIEACH, B. W. (1974). Quantitative studies of microcirculatory structure and function. Circ. Res. 34, 843-857.
The Distensibility of Single Capillaries and Venules in the Cat Mesentery L . H . SMAJE, 1 P. A . FRASER, 2 AND GERALDINE CLOUGH a
Department of Physiology, University College London, Gower Street, London WCIE 6BT Received November 1, 1979 The distensibility of single capillaries and venules of the cat mesentery has been determined using a simple technique in vivo. Selected vessels were occluded under microscopic control and red cell oscillation in the occluded segment was monitored using cinemicrography. The cells were seen to oscillate in synchrony with local vascular pressure which was recorded simultaneously using the servo-null technique. Less than 10% of the oscillation could be accounted for by filtration/reabsorption so the bulk of the movement was thought to be a consequence of distension of the vessel during systole and relaxation during diastole. Changes in radius would be amplified by the factor 2Ur (where r is radius and ~ the length of the occluded vessel) to give the observed movement of red cells. Mean pulse pressure was 3.2 mm Hg in capillaries and 2.3 mm Hg in venules which gave rise to increases in radius of 0.03 and 0.028/zm, respectively. The nature of the structure supporting the vessels was considered and it seemed likely to be the basement membrane which would require a Young's modulus of 1.8 × 106 N m-2 for the capillary and 5.4 × 106 N m-2 for the venule although pericytes might contribute to support of the latter. It is considered likely that some of the higher values quoted in the literature are due to measurements being made at different ends of a nonlinear stress-strain curve, the present data being obtained at the low stresses normally found in mammalian microvessels.
INTRODUCTION
Capillaries are generally thought to be indistensible since increases in transmural pressures of 50 mm Hg (7 kPa) or more produce no observable change in diameter (Baez et al. 1960). Two explanations have been offered to explain this rigidity. One hypothesis views the capillary as a "tube-in-liquid": the capillary walls themselves bear the distending stress because, as a result of their small diameter, the tangential wall tension is very low (Burton, 1954). The alternative point of view, proposed by Fung et al. (1966), considers the capillaries as a "tunnel-in-gel": here support for the capillary is provided by the surrounding gel. The tube-in-liquid hypothesis was criticized on the grounds that the endothelial cell wall and basement membrane would have to have a Young's modulus similar i Present address: Department of Physiology, Charing Cross Hospital Medical School, Fulham Palace Road, London W6 8RF. 2 Present address: Department of Physiology, King's College, Strand, London WC2R 2LS. 3 Medical Research Council Scholar. Present address: University Laboratory of Physiology, South Parks Road, Oxford OXI 3PT. 358 0026-2862/80/060358-13502.00/0 Copyright © 1980by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in U.S.A.
M1CROVASCULAR DISTENSIBILITY
359
to that of collagen. Although Fung et al. (1966) performed some elegant experiments on pieces of mesentery and provided a sophisticated analysis of the data at their disposal, they had no information on the actual distensibility of the capillaries. Instead they accepted the observations of Baez et al. (1960) but assumed an upper limit of distension based on the optical resolution available to Baez et al. A more refined method of measuring capillary distensibility was introduced by Clough et al. (1974), who, on the basis of their measurements, put forward the view that the capillary basement membrane, which contains type IV collagen (Kefalides, 1980), does provide the necessary support. Murphy and Johnson (1975), in a brief review, came to a similar conclusion. More recently, in direct contrast to the findings of Baez et al. (1960), Bouskela and Wiederhielm (1979) showed in a preliminary communication that the diameters of capillaries do increase in response to increases in transmural pressure. Furthermore they calculated that this distensibility is consistent with the basement membrane bearing the stress. In this paper we describe experiments in which the distensibilities of capillaries and venules have been measured by analyzing the oscillations of red cells in microvessels occluded with a small glass needle. From these results we have been able to make estimates of the Young's modulus of elasticity of the vessel walls. METHODS Animals and anesthesia. Experiments were performed on the mesentery of cats of either sex weighing between 1.2 and 2.5 kg. Anesthesia was induced by ethyl chloride and maintained by ether until pentobarbitone (up to 35 mg/kg) could be given via a cannula placed in the femoral vein. Supplementary doses (0.5 ml, 12 mg/ml) were given as required. The trachea and femoral vessels were cannulated routinely. Blood pressure was measured in the abdominal aorta via a Portex (Hythe, Kent) nylon I.V. cannula connected to a pressure transducer (Bell & Howell Type 4-326-L212) and registered on a Devices M4 pen recorder. The cannula and transducer were filled with 0.9% NaCI containing l0 IU heparin/ml. The temperature was maintained at 37° using a heating blanket placed beneath the cat, controlled via a rectal thermistor using the circuit described by Diete-Spiffet al. (1962). Preparation ofmesentery. A longitudinal incision 2-3 cm long was made in the shaved skin over the umbilicus and the animal was laid on its side on a Perspex tray which had a heated side chamber to take the mesenteric preparation. A loop of colon was drawn out of the incision using cotton-wool buds soaked in Krebs solution and its mesentery was placed over a glass-topped pillar in the side chamber positioned above the microscope substage condenser. The intestine rested on cotton-wool soaked in Krebs solution placed around the base of the pillar, and the whole of the exposed tissue was then covered in plastic film (Snappies Cling Film Wrap, Empress Products Ltd.) except for the region of the mesentery under investigation which was irrigated with the Krebs solution. This was composed as follows: NaCI, 118 mM; KCI, 4.7 mM; CaCI2, 2.5 mM; KH2PO4, 1. i mM; MgSO4-7H20, 1.25 mM; NaHCO~, 25 mM; glucose, 11 mM; bubbled with
360
SMAJE, FRASER, AND CLOUGH
95% 02, 5% CO2, and heated to 37° in the final conduit by a stainless-steel heater. This was heated by a resistance wire and controlled by an incorporated thermistor using the circuit of Diete-Spiff et al. (1962), and further checked by a thermistor cemented to the stage beneath the mesentery. The mesentery was irrigated at 4 ml/min using a roller pump and the tube was positioned using a small micromanipulator attached to the animal tray. Microscopy and filming. The tray containing the cat was clamped to a modified stage of a Leitz lntravital microscope equipped with standard Orthoplan optics. The tissue was transilluminated with a Leitz high-pressure 150-W xenon lamp using neutral density filters to adjust the amount of light and a green filter to enhance the contrast of the red cells and to provide monochromatic light for photography. A long-working distance condenser (22 mm) and long-working distance objectives (UM series) were used. The image was split so that light passed through to a binocular viewing head and to an Arriflex H16 16-mm cine camera mounted vertically above the microscope, llford Pan F film was used at 25 frames/sec. Vessels were occluded by glass probes (Micropipettes fused at the tip), held in a Leitz micromanipulator. The probes were pulled from Leitz Pyrex tubing (o.d., 1.2 mm) to give a flexible shank about 15-20/~m in diameter and the tips were fused in a small gas flame to provide a ball 10-50 tzm in diameter. Pressure was measured in the selected vessel by insertion of sharpened glass micropipettes attached to a resistance null-balance servo system of the type described by Wiederhielm et al. (1964) and modified by lntaglietta et al. (1970). Film exposure was determined using a Leitz Microsix exposure meter. Exposed film was developed commercially (Humphrey's Laboratories Ltd.) and frame-byframe analysis undertaken using a PCD XY data reader fitted with a Vanguard 16-mm motion analyzer cine head. Microscope magnification was 160 and the final magnification on the analyzer screen × 1000. The output from the data reader was digitized by a Farnell DCV 100 voltmeter and fed via an 8-channel interface to a Data Dynamics Model 390 teletype and paper tape punch. Vessel radius was measured on the film analyzer. In most experiments a xenon light source was used but in some, red cell position was determined exactly with respect to time by using a stroboscopic light source synchronized to the camera with a simultaneous write out of the pulses on the pen recorder (Clough, 1977). RESULTS Occlusion of the venous end of a capillary leads to movement of the red cells toward the occluding probe. The movement is not smooth but oscillatory, synchronous with the changes in pressure in the supplying arteriole (Fig. 1). Red cells continue to pack down until the plasma colloid osmotic pressure, increased by ultrafiltration, balances the hydrostatic pressure tending to produce filtration. It is important to note that red cell oscillation continues after net movement ceases. This oscillation could be a consequence of either alternate filtration and reabsorption or of distension of the capillary walls during systole and relaxation during diastaole. These alternatives will be examined in turn.
361
MICROVASCULAR DISTENSIBILITY
E
o
2 8 O 2 6 0" 2 4 0
°, . . . .
o
220
200
i
i
1
2 Time
3
Seconds
FI6. I. Oscillatory motion of red cells following occlusion of a single capillary. Dots show individual measurements of column length obtained by frame-by-frame analysis of cine film. The solid line is a fitted monoexponential.
(i) A l t e r n a t e filtration a n d reabsorption
The rate of filtration may be calculated from the equation
Q Jv -
A
- Lp (Pc - IIc),
(1)
where Jv is fluid flux, Q is flow rate, A is exchange area, Lp is filtration coefficient, Pe is capillary hydrostatic pressure, and lie is plasma colloid osmotic pressure. When net red cell m o v e m e n t ceases, mean hydrostatic pressure, Pro, equals II c (see Fraser et al. 1978). The oscillation would then be accounted for by the pulse pressure, AP, where AP = Pc - Pro. Assuming a sinusoidal wave form, fluid m o v e m e n t would thus be L p A P sin tot
Jv -
(2)
2
Red cells in capillaries and venules are good markers of fluid m o v e m e n t (Fraser et al. 1978, and see Discussion) so the oscillatory motion of the red cell due to filtration may be found from J,, A
=
7rr~
d(
Lp A P sin cot
2~r(
dt
2
'
(3)
assuming that the magnitude of oscillation has an insignificant effect on Hc (see Discussion), and, where r is radius of vessel, t ~is length of occluded segment. The distance m o v e d by the red cell (Ag') as a consequence of filtration will be At" = - r
• Lp Ap[ t=Tr sin oJt dt. )t=O
(4)
362
SMAJE, FRASER, AND CLOUGH
This can be shown to be (~Lp AP A(' -
7rrf
'
(5)
where f is pulse frequency. The geometry of the occluded vessel is simply measured and Lp a n d f are obtained by analysis of the occlusion data, Mean red cell movement reflects fluid movement so the mean rate of red cell packing may be used to calculate fluid flux (see Fraser et al. 1978 and Discussion). Initial plasma colloid osmotic pressure is obtained using a plasma sample and Pe is measured by direct puncture. Hydrostatic and colloid osmotic pressures in the interstitium are not taken into account as the values are relatively small (see Clough and Smaje, 1978) and are unlikely to fluctuate with the pulse. Red cell packing rate can be closely approximated by a monoexponential (see Fraser et al. 1978) which was fitted to the data as shown in Fig. 1. The oscillatory component of red cell movement was then extracted by subtracting the exponential curve from the raw data. The frequency of oscillation was obtained simply by measuring the time taken for 6-10 cycles, and the mean change in red cell position A~¢ by averaging the extreme positions in the same cycles. The observed red cell movement, A(, can now be compared with that predicted on the basis of filtration (AC) using the values obtained following occlusion. Table 1 lists these data for both capillaries and venules and it can be seen that the calculated movement, AC, is about 4 and 10%, respectively, of the observed movement, A(. There was no significant difference in A( when determined near the beginning of an occlusion or toward the end when net red cell movement was minimal. Hence alternate filtration-reabsorption cannot be responsible for the major part of red cell oscillation following occlusion.
(ii) M i c r o v e s s e l D i s t e n s i o n
The most likely alternative explanation is distension of the vessel during systole and recoil in diastole. The geometry is simple, as seen in Fig. 2. Ignoring second-order terms, it is assumed that the volume occupied by the changed red cell position, A~Trr2, is accompanied by a slight expansion of the radius of the occluded vessel, Ar and this volume will be 27rrAr~. Equating these gives Ar -
rA~ 2~
(6)
The change in radius is thus amplified by the factor 2(/r. Assuming a minimum resolution for A( of about I txm and a typical capillary length of 100-200/~m, this allows measurement of a change in radius of 0.01 /zm or less, well below the resolution of the light microscope. The mean values for the change in radius in capillaries and venules in the present experiments were 0.030 and 0.028 tzm as seen in Table 1. It is now possible to calculate compliance of the vessel wall. If the vessel is considered to be a tube in liquid and the wall as a whole is withstanding the applied
363
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364
SMAJE, FRASER, A N D CLOUGH
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pressure, then the incremental Young's modulus Ein c of the wall can be determined from E = A stress/A strain. By using the Laplace relationship (P = T/r): Einc =
A stress A strain
APr
1
=
APr 2
1
- -
Ar/r
x
°
Ar
_
_
x
,
(7)
where x is thickness of supporting structure in the wall. Values of Ein~C (Young's modulus × wall thickness) are listed in Column l0 of Table I. Ein~X is a composite value making no assumptions about the structure(s) supporting the wall except that the support is coming from the wall itself rather than the surroundings. Laplace's law obviously only approximates to the situation and the walls cannot be considered to be thin relative to the diameter. The value for Einc may be calculated using a formulation for thick-walled tubes (Love, 1927) as follows: AP Ein e = ~
Ar
2(1 - o"z) rl 2 (rl + x) (rl + x)~ - rl 2
,
(8)
where rl is internal radius and ~ is Poisson's ratio, assumed to be 0.5. The values calculated using L o v e ' s equation differ somewhat from the simple application of Laplace's law but are of a similar order of magnitude. Table 2 shows values calculated for Ein~ using the mean data obtained from Table I and Eq. (8) and assuming that support for the vessel is coming from the layer of the wall specified in Table 2. The alternative "tunnel in gel" hypothesis may be approximated by considering the mesentery to be a thick tube surrounding the vessel whose inside radius is the measured value and whose wall thickness x is (z - r)/2, where z is the mesentery thickness. Using Eq. (8) and a mesentery thickness of 70/~m, Eine for capillaries and venules is 1.04 × l04 and 3.22 x l04 N m -2, respectively. DISCUSSION The present results need to be compared with data derived from the perfusion experiments of Baez et al. (1960) and from the calculations of compliance based
MICROVASCULAR
365
DISTENSIBILITY
TABLE 2 CALCULATIONS FOR YOUNG'S MODULUS FOR STRUCTURES OF THE VESSEL WALL BASED ON THE ASSUMPTION THAT THE STRUCTURE CONCERNED ALONE PROVIDES SUPPORT
Capillaries
Whole wall Endothelium Basement membrane Whole mesentery
Venules
X
Ein e
X
Etn e
~m)
(N m-~)
~m)
(N m-2)
1.5 0.4
3.88 × 1@ 1.4 x 106
0.1
5.4
0.5 0.3
3.7
0.1
1.8
31
× 1@ 6.1@ x 106
1.04 x 104
27
x 106
3.22 x 104
Note. A p p r o p r i a t e m e a n v a l u e s f r o m T a b l e 1 t o g e t h e r w i t h v a l u e s of t h i c k n e s s f r o m the l i t e r a t u r e are u s e d for s u b s t i t u t i o n into Eq. (8).
on measurements of pulse velocity in the microcirculation undertaken by Intaglietta et al. (1971). However, the validity of the present measurements will be assessed before they are interpreted in relation to theories attempting to account for microvascular rigidity and the known structure of the capillary and venular walls. Validity o f the Present Measurements
We have a method of measuring capillary and venular distensibility which is critically dependent on the assumption that the movement of red cells accurately reflects the motion of the plasma. This problem has been considered previously (Fraser et al., 1978) and it was established that the net cell motion did indeed reflect the transendothelial fluid flux. All the vessels studied had larger diameters than red cells (i.e., positive clearance) so that the situation in which lubrication theory (Fitz-Gerald, 1969) must be considered, does not apply. In addition platelets were observed, on occasion, within the occluded capillary segments, and they moved with the red cells. However, velocity at the wall must be zero and thus red cell velocity will overestimate mean plasma flow to some extent. Even in freely flowing capillaries red cell velocity is only 1.3 times that of mean velocity (Gaehtgens et al., 1976; Lipowsky and Zweifach, 1978) and the undistorted shape of red cells in the present situation means that the overestimate will be even less and the measurements of Einc underestimated in proportion. The curve for red cell column length vs time is fitted well by a monoexponential in many capillaries (e.g., Fig. 1) but it is a less satisfactory fit for very permeable vessels and those in which there is a very small equilibrium relative cell separation (¢0/¢oo <0.8). In applying the technique generally, therefore, difficulties could arise with some vessels. Although no conscious selection occurred in the present experiments, it should be pointed out that the present values for Lp are lower than those obtained in a previous study in the cat mesentery (Fraser et al., 1978). It is likely that this
366
SMAJE, FRASER, AND CLOUGH
represents a sampling problem. If the previous Lp values are taken to be representative of the microvasculature as a whole, then filtration/reabsorption accounts for a somewhat larger proportion of red cell movement than calculated here. The proportions increase from 4 and 10% in capillaries and venules, respectively, to 10 and 12%. This still indicates that filtration/reabsorption makes a minor contribution to red cell oscillation and does not affect our main conclusions. A further assumption in our analyses is that IIc does not change significantly during individual red cell oscillations (Eq. (4)). The relationship Lp AP/Ilrf gives the proportionate increase in protein concentration during the half cycle. This gives a fractional increase of 0.0014 and even assuming a protein concentration of 10% at equilibrium, an unlikely high value, such an increase in concentration does not lead to a significant increase in IIc and our assumption is seen to be valid.
Rigidity of the Microvascular Wall If we begin by assuming that the capillary wall, or some part of the wall, provides the necessary support then Young's modulus may be obtained by dividing the values for Ein~X in column 10 of Table 1 by the thickness of the layer concerned, x, or more accurately by using Love's formula (Eq. (8) vs). There seems to be some doubt about the thickness of the basement membrane as quoted values vary from 0.02 to 0.18/~m but a reasonable value for the present purposes would be 0. I/~m (Williamson et al. 1969). No data are available for the thickness of venular basement membrane but they are assumed to be the same as those for capillaries. This value, together with those obtained by Rhodin (1968) for capillary and venular dimensions of the whole vessel and of its endothelium are used in Table 2 for calculations of Young's modulus using Love's equation. It can be seen that Young's modulus for capillaries and venules are similar if the whole wall is considered the supporting structure, but if support comes from the endothelium or basement membrane alone or is provided by the interstitium, different values are found for the two types of vessel. This aspect of the study will be considered later, but meanwhile a comparison of the present values with data in the literature is of interest. From Table I it is seen that the mean change in capillary radius was 0.03/~m for an increase in hydrostatic pressure of 3.36 mm Hg. On this basis, an increase in diameter of 1.8 p.m would have been expected for the transmural pressure increase of 60 mm Hg employed by Baez et al. (1960) whereas no increase was detected. The most likely explanation for this apparent discrepancy is that capillaries have a nonlinear stress-strain relationship, the stress increasing disproportionately at higher strains. This was observed with arterioles (Wiederhielm, 1965) and capillaries (Bouskela and Wiederhielm, 1979). With increasing distension, arteriolar walls become stiffer, Young's modulus for the wall varying from about I x 105 N m-2 at 5% above normal strain to about 45 × l0 s N m -2 at 30% above normal strain. Similarly, reducing pressure below 15 mm Hg led to a fall in vessel diameter in the experiments of Baez et al. (1960) but these authors attributed this to critical closure of the vessels. Unfortunately, insufficient points on the pressure-diameter relationship were obtained to be sure of the interpretation. However, a range of pressure-diameter values is available for renal tubule and
367
MICROVASCULAR D I S T E N S I B I L I T Y
isolated renal tubule basement membrane. Young's modulus varies from about 3.3 x 10n N m -2 at pressures between 10and 30 mm Hg to 5.7 x 106 N m -2 for pressures between 30 and 60 mm Hg for both intact tubule and for isolated basement membrane (calculated from Welling and Grantham, 1972). Collagen is well known to show stiffening at higher strains (Burton, 1954) and it seems reasonable to conclude that collagen in the basement membrane or elsewhere in the microvessel wall may well be responsible for the nonlinear stress-strain relationship of such vessels. However, Fung et al. (1966) also found marked nonlinearity for rabbit mesentery but this tissue too contains collagen (about 15% according to Fung et al.). As can be seen in Table 3, the absolute magnitude of the Young's modulus obtained for the whole wall in the present experiments is comparable with those obtained for arterioles at low strains but less than that suggested by Fung et al. (1966) on the basis of their analysis of their own data and that of Baez et al. (i 960). It is more difficult to reconcile our findings with those of lntaglietta et al. (1971), who calculated a much lower Young's modulus. They explained the high compliance value they calculated from pressure pulse velocity across the microcirculation as being chiefly due to the distorting effect of red cell oscillation caused by filtration-absorption. We have shown from our measurements of pressure and filtration coefficients, however, that filtrationreabsorption can account for merely 4-10% of the oscillation (Table 1). If filtration-reabsorption were the explanation, backward movement of the red cells during an occlusion would occur only if diastolic pressure decreased below plasma colloid osmotic pressure. The available evidence suggests that this does not
TABLE 3 VALUES FOR YOUNG'S MODULES OF CERTAIN TISSUES FOR COMPARISON WITH PRESENT VALUES Young's modulus (N m 2) Structure Cat mesenteric capillaries (a) Whole wall (b) Basement membrane Cat omental capillaries Whole wall Frog mesenteric arterioles Whole wall Whole mesentery Renal tubule basement membrane Lens capsule basement membrane Collagen
Authors
Low strain
High strain
Present 3.7 x 10~ 1.8 × 10~ lntaglietta et al. 1971 (Recalculated)
Wiederhielm, 1965 Fung et al., 1966 Welling and Grantham, 1972 Fisher and Wakely, 1976 Bergel, 1961
1.5 x 1@
1.2 × 1@ 0.9 x l(P
4.5 x 106 1.8 x 106
3.3 × 10~
5.7 × 106
0.8 x l0n 1 × 107
7.7 x l0 n lxl0 ~
368
SMAJE, FRASER, AND CLOUGH
happen in freely flowing vessels in the mesentery (Zweifach, 1964; Fraser et al. 1978). Since filtration/reabsorption can account for only about 10% of red cell oscillation, the very high compliance found by lntaglietta et al. (1971) needs to be explained. Their value for Young's modulus, 4.5 × 104 N m-2 for the whole wall is certainly less than the usually quoted values but it was obtained at normal pressures and should thus be compared with our value of 3.7 × 1@ N m-2. In their calculations they used a ratio of radius:wall thickness of l:9 based on the measurements of Baez (1969). These do not accord with electron microscopical measurements (Rhodin, 1968; Simionescu et al. 1975) and a ratio of about 10 would appear more appropriate. If this value is used the Young's modulus becomes 1.5 × 105 N m -2, which completely alters the interpretation of their data and is remarkably close to the present value. It should be noted that our calculations assume isotropy and no change in vessel length. No changes were observed so the assumption seems reasonable.
Structure Responsible f o r Support
Endothelial cells are generally thought to have little resistance to deformation (see Fung et al. 1966) and are unlikely to provide the necessary support. Certainly the presence of renal tubular epithelial cells makes no difference to the distensibility of renal tubules, the support for which comes from their basement membrane (Welling and Grantham, 1972). If basement membrane were responsible in capillaries as well, it would require a Young's modulus of i.8 × 1@ N m-z, which is similar to the value found for renal tubule and lens capsule basement membranes (Fisher and Wakely, 1976; see Table 3). These values are below the range quoted for collagen (3-100 x 106 N m-Z; Bergel, 1961) but if the basement membrane were thinner than the value used for the present calculations, as is possible, then our values would fall within the lower end of the range. Fisher and Wakely (1976) found that lens capsule basement membrane had a lower Young's modulus than collagen but calculated that the filaments from which the basement membrane and collagen were formed had the same elastic moduli. The difference in measured Young's moduli was explained partly by filament arrangement and partly by differences in the angle of tilt of the helices of individual filaments while the nonlinear stress-strain relationship was thought to be a consequence of the uncoiling of the helices. Williamson et al. (1969) made the interesting observation that capillary basement membrane thickness is correlated with transmural hydrostatic pressure which suggests that basement membrane has an important role in the support of capillaries. The higher value for EineX in venules could be accounted for if the basement membrane were thicker in these vessels, although there is no information on this point, or it could be due to the presence of the pericytes and the tethering effects of their associated collagen fibrils (see Rhodin, 1968). While the overall value for vessel distensibility found here could certainly be provided by support from the surrounding gel, the larger diameter of venules would predict a greater distensibility and a similar Young's modulus, whereas we found venules to have a greater Young's modulus. Furthermore, if the interstitium did provide support, our somewhat simple calculations suggest that the Young's
MICROVASCULAR DISTENSIBILITY
369
modulus determined by Fung et al. (1966) is too high. However, the detailed arrangement of collagen within the mesentery is not known and, as pointed out by Fung et al. (1966), it is necessary to know the detailed structure of complex tissues before their mechanical characteristics can be computed. The present experiments thus provide a technique for measuring distensibility in single capillaries and venules and tend to suggest that the basement membrane and pericytes are responsible for support. Our calculations also suggest that the microvessels are normally acting at a low point in their stress-strain relationship and that the high values often quoted are a consequence of measurements taken at higher parts of the nonlinear stress-strain relationship. APPENDIX 1: LIST OF SYMBOLS
JV
Q
A Lo Pc Pm AP Hc r Ar rl
t At At'
f o) x (7.
t z
Einc
rate of volume flux rate of fluid flow out of occluded segment surface area filtration coefficient capillary hydrostatic pressure mean capillary hydrostatic pressure pulse pressure plasma colloid osmotic pressure vessel radius change in radius internal radius length of occluded segment red cell oscillation distance moved by red cell as a consequence of filtration pulse frequency angular velocity thickness of supporting structure in wall Poisson's ratio time thickness of mesentery incremental Young's modulus ACKNOWLEDGMENTS
The British Heart Foundation is gratefully acknowledged for a project grant to L. H. S. We are most grateful to Mr. S. R. Rawlinson for his expert technical assistance and to Dr. D. H. Bergel for his helpful criticism of the manuscript.
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