effect of sarcomere length on total capillary length in skeletal muscle: in vivo evidence for...

MICROVASCULAR RESEARCH 40, 63-72 (1990)

Effect of Sarcomere Length on Total Capillary Length in Skeletal Muscle: /n Viva Evidence for Longitudinal

Stretching of Capillaries

C. G. ELLIS, 0. MATHIEU-COSTELLO,* R. F. POTTER, I. C. MACDONALD, AND A. C. GROOM

Department of Medical Biophysics, University of Western Ontario, and The John P. Robarts Research Institute, London, Ontario, N6A SC1 Canada; and *Department of Medicine,

M-023, University of California, San Diego, California 92093

Received June 14, 1989

It is generally assumed that when a muscle is shortened or extended the total length of capillaries does not change, implying that capillaries are nondistensible, longitudinally. On the basis of stereological estimates of capillary anisotropy versus sarcomere length, we propose that as long as capillaries are in a tortuous configuration muscle extension will merely decrease the tortuosity, leaving vessel length unaltered. Once capillaries have been pulled into a straight configuration, further extension of the muscle will cause the vessels to stretch. By means of intravital videomicroscopy we have demonstrated that stretching of individual capillaries does indeed occur over a sarcomere length range of 2.1 to 2.9 pm in rat extensor digitorum longus muscle. In vivo measurements of the lengths of six capillaries together with the sarcomere lengths of adjacent fibers were made in muscles positioned at various degrees of extension. Normalized data indicated that four capillaries stretched to the same degree as the muscle, one stretched more and another less. This may reflect differences in distensibility or tortuosity of capillaries in series with one another. The elastic stretching of capillaries during muscle activity may have important conse- quences in terms of shifts in permeability and increases in capillary surface area. o 1990 Academic Press, Inc.

INTRODUCTION

A dramatic change in capillary configuration accompanies the shortening of skeletal muscle. As was shown initially by Potter and Groom (1983), the capillaries running parallel to the muscle fibers in extended muscles are relatively straight whereas in shortened muscles they are very tortuous. Recently, we examined this behaviour quantitatively as a function of sarcomere length (Ma- thieu-Costello et al., 1988), using stereological estimates of K, the degree of capillary anisotropy and c(K,O) the coefficient relating capillary density in transverse section, Q*(O), to capillary length density, JJc,f), as described by Mathieu- Costello et al. (1983). This analysis showed that the capillaries running alongside muscle fibers adopted an increasingly tortuous configuration as the sarcomere length decreased. We interpreted this to mean that “as the muscle shortens the total length of the capillary network remains the same, and the capillary segments

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64 ELLIS ET AL

are forced to adopt an increasingly tortuous configuration, confined within the space between muscle fibers.” This interpretation was based on the generally accepted view that capillaries are nondistensible; that is, the capillary length density of a particular muscle is independent of sarcomere length.

In our previous paper (Mathieu-Costello et al., 1988), we noted that both K and c(K,O) approached limiting values as the muscle was extended. We interpreted that these limiting values were determined by the presence of anastomoses between capillaries aligned with the axis of the muscle fibres, since these anastomotic vessels could never adopt the same orientation as the parallel capillaries. Further examination of this stereological data, however, reveals that there was very little change in capillary anisotropy and tortuosity for sarcomere lengths, (I,,), over the range from 2.5 to 3.5 pm. This means that the parallel capillaries which had become almost entirely straight and aligned with the fibers at lo = 2.5 pm were still able to accommodate a further 40% increase in sarcomere length. How is this possible? One explanation which would maintain capillary length density constant, would be that the collagen matrix tethering the capillaries to the muscle fibers is extremely loose or distensible, thus allowing the capillaries (and the arterioles and venules to which the capillaries are attached) to slip relative to the muscle as it is extended. However, a consequence would be that some regions of the muscle must undergo a dramatic decrease in capillary density, Q*(O). A or 1 k 1 m e i e y explanation is that the capillaries themselves are able to stretch in proportion to the muscle extension. This implies that capillary length density, capillary surface area, and possibly capillary permeability are functions of sarcomere length above some value of lo.

On the basis of the concept that capillaries stretch in extended muscles, we propose the following simple physical model for individual capillaries in skeletal muscle. As long as capillaries are in a tortuous configuration, muscle extension will merely cause them to become less tortuous with no change in vessel length. Once capillaries have been pulled into a straight configuration, muscle extension will result in capillary stretching and a linear increase of individual vessel length with 1,.

The goal of this paper was to test our hypothesis that capillaries can stretch longitudinally in viva. The paper is divided into two sections. First, we inves- tigated whether our physical model is supported quantitatively by the stereological data. Second, we used intravital microscopy to measure the length of individual capillaries as a muscle is extended in a graded fashion, to determine whether there is evidence which supports the concept of the elastic stretching of capillaries.

Physical Model of Capillary Behaviour as a Function of Sarcomere Length

The physical model we propose can be expressed as

JV(c,fl = constant, for lo < lB

and

J”(C,rf) Oc 4% for lo 2 lB)

where 1, is the sarcomere length at which capillaries, being fully straightened, can accommodate further muscle extension only by stretching longitudinally.

CAPILLARY STRETCHING IN MUSCLE IN VW0 65

This model assumes that all capillaries are fully straightened at the same sarcomere length and that the contribution of anastomotic vessels to JJc,f) is independent of sarcomere length.

The model cannot be tested by a direct comparison between JJc,j) and lo from our previously published data. The morphometric analysis of capillary geometry required vascular perfusion fixation of the muscle, thereby restricting examination of each muscle to only one sarcomere length. Hence, our data on JJc,j) and lo were obtained from different limbs and/or animals. This introduces substantial differences in fiber size and capillary-to-fiber ratio between samples, even at the same sarcomere length, leading to considerable scatter in the estimates of both capillary density, Q*(O), and JV(c,f). In contrast, measurements of K and c(K,O) in each muscle are not affected in this way, because they are based on the ratio between capillary counts in transverse versus longitudinal sections in each specimen. Some differences are to be expected even in c(K,O) values at the same l,, because of variations in capillary branching among muscles.

For each muscle, the model can be rewritten using the equation (Mathieu et al., 1983):

cW,O) = Jv(c,f) / QA@). During muscle shortening/extension in viva the product of mean fiber cross- sectional area and muscle length must remain constant (conservation of mass), as must the number of capillaries in a transverse section of the entire muscle. Therefore, for any particular muscle Q,+(O) will vary directly with lo. Thus the physical model predicts that

and

c(K,O) = constant, for lo > lg.

As a first approximation, we tested the model using the most complete set of stereological data currently available for c(K,O) in a single species (rat hindlimb muscles; Mathieu-Costello, 1987; Mathieu-Costello et al., 1988; Poole et al., 1989; Poole and Mathieu-Costello, 1989) by means of a piecewise regression analysis. Our purpose was to determine whether: (1) the stereological data on capillary orientation, obtained from a population of capillaries in each sample, were compatible with our simple physical model; and (2) a value of iB could be approximated for the population of muscles. The regression model was

where b and lB are parameters determined using a microcomputer-based statistical program (Systat: Wilkinson, 1988). The conditional expressions enclosed in pa- rentheses in the above equation have the value unity when true and zero when false. Figure 1 shows the fit of the physical model to the stereological data. The analysis revealed that b = 2.58 pm (95% confidence limits 2.52 to 2.64 pm), and that fB = 2.26 pm (95% confidence limits 2.14 to 2.38 pm).

Using the fitted model we may predict that capillary length density should remain constant for sarcomere lengths less than 2.26 pm, and increase linearily for sarcomere lengths greater than this value. This is illustrated in Fig. 2, which

ELLIS ET AL.

1.25

2.0 2.5 3.0 3.5

Sarcomere Length (pm) FIG. 1. The solid curve is the fit of the physical model to the stereological data (open circles)

of c(K,O) versus sarcomere length for rat hindlimb muscles (see Mathieu-Costello, 1987; Mathieu- Costello et al., 1988; Poole et al., 1989; Poole and Mathieu-Costello, 1989).

shows the percentage change in JJc,f) to be expected. Although the model is consistent with the stereological data, this does not prove that our hypothesis is correct. The next step was to verify experimentally that capillaries do indeed stretch within the range of sarcomere lengths encountered in viva.

Experimental VeriJication of Capillary Stretching

Using intravital video microscopy, we can measure the lengths of individual capillaries as a muscle is extended over a range of sarcomere lengths. To do this, one needs to measure the distance between two fixed reference points along the length of each capillary under study, at different sarcomere lengths. For this purpose, we have used the distance between successive capillary bifurcations (interbranch length) for capillaries aligned with the axis of the muscle fibers.

METHODS

Three male Wistar rats weighing 100 to 150 g were anesthetized with sodium pentobarbital (6.5 mg/lOO g, ip). Following induction of anesthesia the extensor digitorum longus (EDL) muscle was exposed by reflection of the overlying muscles. Its distal tendon was dissected free of connective tissue, allowing a silk suture to be tied securely around the tendon prior to freeing it from its bony insertion. The free end of the suture was then attached to a mechanical device (Burleigh “Inchworm”) which was used to stretch the muscle in a graded fashion. The entire muscle preparation was covered with Saran wrap to prevent evap- oration. The rat was placed on the stage of a Leitz intravital microscope (Model ELR) equipped with an MT1 television camera (Model CC-67ML). The EDL muscle was transilluminated by positioning the end of a fiber-optic light guide equipped with a glass prism beneath the muscle. The source of illumination was a Schott KL 1500 lamphouse with a 150 W halogen light bulb, equipped with a heat filter. Video recordings of selected views of capillaries and surrounding muscle fibers were made following sequential lengthening of the muscle, using


Sarcomere Length (pm)

FIG. 2. The percentage change in capillary length density, J&J), predicted from the relationships shown in Fig. 1, plotted over the full range of sarcomere lengths.

a Panasonic NV-9240XD video recorder. At the completion of each experiment a micrometer scale was also recorded.

Capillaries suitable for analysis were selected on the basis of several criteria: (1) they had to be straight (i.e., no undulations) and parallel to the surrounding muscle fibers, (2) they had to have at least two branches which remained within the field of view during the extension of the muscle, and (3) sarcomeres within the adjacent muscle fibers had to be clearly visible. Photographs of the capillaries and the surrounding muscle fibers were taken directly from the video monitor both prior to and following the sequential lengthening of the muscle. The photographs were enlarged by projecting the image of the capillaries onto a flat surface using a photographic enlarger (Omega 2D). From such enlarged images measurements of the linear distance between two successive branch points (interbranch distance) were made by positioning the points of a calliper at the centres of the two branch points. Sarcomere lengths were determined by mea- suring the combined length of at least 10 sarcomeres, and only those sarcomeres which were immediately adjacent to the capillary segment of interest were measured. The length per sarcomere was then calculated.

RESULTS

Measurements of interbranch distance which were obtained following sequential lengthening of the muscle are shown, as a function of sarcomere length, for six capillaries in Fig. 3. These data were all taken within the range of sarcomere lengths for which our physical model predicts an increase in capillary length density as the hindlimb muscles of the rat are extended (see Fig. 2). At the magnification employed, the maximum interbranch distance that could be vis- ualized on the monitor was 200 pm (approx). It appears from Fig. 3 that for each increase in sarcomere length there was a corresponding increase in interbranch distance for each capillary. Nevertheless, the wide range of initial interbranch distances (30 to 160 pm) made comparison between capillaries difficult. For this reason, both interbranch distance and sarcomere length measurements were normalized with respect to their values at a sarcomere length of 2.5 pm

68 ELLIS ET AL.

2.0 2.2 2.4 2.6 2.6

Sarcomere Length (pm)

FIG. 3. The lengths of capillaries measured from rat extensor digitorum longus muscle, using intravital videomicroscopic techniques, are plotted as a function of sarcomere length. The different symbols represent individual capillaries. For each capillary the relationship between capillary and sarcomere lengths was described by fitting the data using least squares linear regression. Capillary length refers to the interbranch distance (see text).

(chosen arbitrarily as approximately the midpoint of the range of sarcomere lengths used in this study). Figures 4a and 4b are plotted on this basis.

In Fig. 4a all the data are plotted simply in the form of a scattergraph, whereas in Fig. 4b the data for each capillary are distinguished. When the data are plotted in a normalized fashion (Figs. 4a and 4b), the line of identity (dashed line) represents a 1: 1 relationship between the stretching of a capillary and the extension of the muscle. The regression line obtained by a least squares analysis of all the data (Fig. 4a; r = 0.90; P < 0.0005) has a slope and intercept not significantly different from unity and zero, respectively (P > 0.05). An unweighted regression analysis of the data was used, since the distribution of the residuals of interbranch distance obtained from the regression analysis was found to be independent of sarcomere length. Figure 4b shows that not all of the six capillaries showed a slope of unity. The analysis in Table 1 reveals that for one capillary the slope of the regression line was significantly greater than unity, while for one other capillary the slope was significantly less than unity. This result is surprising, for it means that one capillary actually stretched more than its adjacent muscle fibers did, whereas another stretched less.

DISCUSSION

Stereological Prediction of Capillary Distension

The physical model presented here is a first-order approximation for the behaviour of a population of capillaries in a single muscle over the range of sarcomere lengths found in vivo. This model assumes that within this population all capillaries which are aligned with the muscle fibers have the same lB and the same functional relationship with sarcomere length. However, microcorrosion casts (Potter and Groom, 1983) and intravital videomicroscopy both show that it is possible to have tortuous capillaries and straight capillaries adjacent to the same muscle fiber. This means that the onset of stretching (transition from sinuous


0;8 1.0 1.2

h /

/ 0.84

0.8 1.0 1.2

Normalized Sarcomere Length

FIG. 4. Normalized capillary lengths (normalized interbranch distances) are plotted versus normalized sarcomere lengths (a) as a scattergraph of all data pooled from the extensor digitorum longus muscles, and (b) as a graph of the individual capillaries. The dashed line in each figure represents the 1: 1 relationship between capillary and muscle fiber lengths, the solid lines represent the regression lines for each set of data. The slope of the regression line shown in (a) was not significantly different from the line of identity, P > 0.05. The slopes of the regression lines for the individual capillaries shown in (b) illustrate the variations encountered in capillary stretch with respect to the extension of the muscle.

to straight) would not occur at the same sarcomere length for all capillaries. Thus, a higher order model of capillary behaviour would include a distribution of 1, values for a particular muscle. In addition, the experimental data from this study have shown that not all capillaries stretch to the same degree as the muscle. Thus future models also need to incorporate statistical information on this behaviour. We can speculate that the integrated response of all of these factors will result in a smooth transition in the predicted behaviour of c(K,O) and JV(c,f) in the neighbourhood of 1, shown in Figs. 1 and 2 rather than the discontinuous slope our current model predicts. In fact, the resulting curve for c(K,O) would likely be very similar to the empirical curve for c(K,O) versus lB presented in previous papers (Fig. 6, Mathieu-Costello ef al., 1988; Fig. 4, Poole et al., 1989; Fig. 1, Poole and Mathieu-Costello, 1989). It should be emphasized that since there exists a large range of sarcomere lengths over which capillary tortuosity does not change, the prediction that capillaries should stretch longitudinally when muscle is extended will always remain.

Our fit of the physical model to the stereological data for c(K,O) assumes that the data are representative of the behaviour of all capillary segments in a single muscle over the entire range of sarcomere lengths. In reality, each c(K,O) value

70 ELLIS ET AL.

TABLE 1 COMPARISON BETWEEN THE STRETCH OF THE CAPILLARIES AND THE MUSCLE

Plot t Degrees of

statistic freedom Probability Degree of stretch

2.350

0.201

0.324

10.587

2.140

0.785

P < 0.05 Capillary > muscle

P > 0.05 Capillary = muscle


P < 0.05 Capillary < muscle



Note. Comparison of the slopes of the regression lines for the individual capillaries, shown in Fig. 4b, with the line of identity using an unpaired Student’s t test.

was obtained in a different muscle fixed at a given sarcomere length. We have assumed that all muscle samples from the hindlimb of the rat would show the same c(K,O) behaviour with sarcomere length. Obviously, factors such as the relative number, length, and orientation of capillary segments and anastomotic vessels in different muscle samples will lead to different c(K,O) curves for each muscle and may account for the scatter of values seen in Fig. 1. Until we are able to measure either c(K,O) or JJc,f) versus I0 in a single muscle we will be limited to using data, obtained from many muscles, to fit our models. Intrinsic intermuscle differences in capillary geometry make it difficult to define and/or distinguish between higher order models or model parameters.

In a study designed to explore different fixation methods for muscle samples from large animals, it was found that capillary length density increased by 41% between samples, from the same muscle in horse, fixed in situ during flexion (I0 = 1.85 pm) and extension (lo = 3.0 pm), respectively (Mermod er al., 1988). The authors suggested that whereas this result could be due to sampling from two different locations on the surface of the same muscle, it was more likely that “during maximal extension capillaries might be stretched to some degree.” If the predictions of our physical model based on stereological data from the rat hindlimb muscles (Fig. 2) applied also to equine muscles then capillary length density in equine muscle at lo = 1.85 pm should be at its minimum value. Extending the muscle to I,, = 3.0 pm should increase capillary length density by 33%. Our predictions based on hindlimb muscles of the rat are in good agreement with the results of Mermod and co-workers for equine muscle.

Zntravital Videomicroscopic Measurement of Capillary Stretching

The second objective of this paper was to test experimentally the hypothesis of capillary stretching using intravital videomicroscopy. Due to limitations im- posed by intravital microscopy, we were restricted to studying capillaries over a range of sarcomere lengths from 2.1 to 2.9 pm (approx). This is the range over which both sinuous and straight capillaries are present, but for this study mea-

CAPILLARY STRETCHING IN MUSCLE IN WV0 71

surements were taken from straight vessels exclusively. On the basis of the physical model, we expected that mechanical extension of the muscle would result in stretching of these capillaries in direct proportion to the degree of muscle extension. This was confirmed experimentally by the 1: 1 relationship between normalized values of capillary and sarcomere length. These results provide direct evidence for the longitudinal distensibility of capillaries in skeletal muscle in viva and, thus, for an increase in capillary length density with sarcomere length.

We had expected that each individual capillary would stretch in a direct 1: 1 relationship to changes in sarcomere length. Therefore, we were surprised to find that one capillary stretched more, and another less, than the muscle. Such differences may reflect the presence of capillaries, in series with one another, which have differences either in distensibility or degree of tortuosity. Differences in capillary distensibility may occur due to variations in vessel diameter, wall thickness, and degree of tethering to adjacent myocytes. For example, variations in capillary diameter have been shown to occur not only spatially throughout the muscle (Potter and Groom, 1983; Groom, Ellis and Potter, 1984), but also along the length of the capillary (Ellis et al., 1989). Also, if a tortuous capillary were in series with the straight capillary being measured, then extension of the muscle would not necessarily result in elastic deformation of the straight capillary, until straightening of the tortuous capillary had occurred.

Physiological Implications

The concept of capillary stretching during changes in muscle length may have important implications for microvascular blood flow and the transport of materials across the capillary wall. For example, does the volume of the capillary network increase or remain constant as the capillaries are stretched? If the volume remains constant the capillary diameter must decrease, potentially causing considerable increase in flow resistance. Does the capillary wall accommodate stretching by the movement of endothelial cells, for example, by the sliding and potential separation of the overlapping edges of adjacent cells? If so, this has the potential to increase both the permeability and the capillary surface area. The ability of the capillaries to become sinuous when the muscle is shortened may be an important mechanism employed to overcome the problems associated with elastic stretching of capillaries. It is possible that a muscle normally functions about a sarcomere length at which some degree of tortuosity exists, and thus capillaries may be extended over a small range of capillary lengths without the need for elastic stretching of their wall.

CONCLUSION

On the basis of the stereological estimates of c(K,O) versus lo it was predicted that capillary length density would depend directly on the length of the muscle above a particular sarcomere length, lg. We proposed a simple physical model which describes this behaviour. Using piecewise regression analysis we found that (1) the stereological data were compatible with the model, and (2) it could be predicted that overall, in the population of muscles compared, capillaries should stretch above a sarcomere length of 2.26 pm. The prediction that capillaries stretch during muscle extension for lo > 2.26 pm was confirmed in rat

72 ELLIS ET AL.

EDL muscle by direct intravital microscopic measurements of capillary length. What we did not anticipate, however, was the variation in the response of individual capillaries to the extension of muscle fibers (Fig. 4b). Such variations suggest that some capillaries stretched to the same degree as the surrounding muscle fibers, while others had either a higher or lower compliance to muscle extension. Further studies on the differential lengthening of capillaries are nec- essary before the physiological significance of capillary distensibility can be understood. In particular, the variation in the response of capillary diameter and ultrastructure to muscle extension must be studied in terms of the effects on blood flow and exchange of materials within the microvasculature of the muscle.

ACKNOWLEDGMENTS

We are grateful to Mrs. Barbara Anderson for typing this manuscript. This work was supported by the Heart and Stroke Foundation of Ontario and by Grants 5 PO1 HL-17731 and HL-01534 from the National Institute of Health. Dr. C. G. Ellis is an HSFO Scholar. All statistical calculations were performed using Systat; all Figures and Tables were produced using Sigmaplot and Core1 Draw.

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GROOM, A. C., ELLIS, C. G., AND POTTER, R. F. (1984). Microvascular architecture and red cell perfusion in skeletal muscle: Changes during shortening and possible improvement in oxygen transport to tissue. Prog. Appl. Microcirc. 5, 64-83.

MATHIEU, 0. CRUZ-ORIVE, L. M., HOPPELER, H., AND WEIBEL, E. R. (1983). Estimating length density and quantifying anisotropy in skeletal muscle capillaries. J. Microscopy 131, 131-146.

MATHIEU-COSTELLO, 0. (1987). Capillary tortuosity and degree of contraction or extension of skeletal muscles. Microvusc. Res. 33, 98-117.

MATHIEU-COSTELLO, O., POTTER, R. F., ELLIS, C. G., AND GROOM, A. C. (1988). Capillary configuration and fiber shortening in muscles of the rat hindlimb: Correlation between corrosion casts and stereological measurements. Microvasc. Res. 36, 40-55.

MATHIEU-COSTELLO, O., HOPPELER, H., AND WEIBEL, E. R. (1989). Capillary tortuosity in skeletal muscles of mammals depends on muscle contraction. J. Appl. Physiol. 66(3), 1436-1442.

MERMOD, I., HOPPELER, H., KAYER, S. R., STRAUB, R., AND WEIBEL, E. R. (1988). Variability of fiber size, capillary density and capillary length related to horse muscle fixation procedures. Acta Anat. 133, 89-95.

POOLE, D. C., AND MATHIEU-COSTELLO, 0. (1989). Skeletal muscle capillary geometry: Adaptation to hypoxia. Resp. Physiol. 17, 21-30.

POOLE, D. C., MATHIEU-COSTELLO, O., AND WEST, J. B. (1989). Capillary tortuosity in rat soleus muscle is not affected by endurance training. Amer. J. Physiol. 256 (Heart Circ. Physiol. 25): HlllO-H1116.

POTTER, R. F., AND GROOM, A. C. (1983). Capillary diameter and geometry in cardiac and skeletal muscle studied by means of corrosion casts. Microvusc. Res. 25, 68-84.

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effect of sarcomere length on total capillary length in skeletal muscle: in vivo evidence for...

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