The microvasculature in skeletal muscle

MICROVASCULAR

RESEARCH 30,

29-44 (1985)

The Microvasculature

in Skeletal

I. Arteriolar Network in Rat Spinotrapezius ERIK

Muscle Muscle’

T. ENGELSON, THOMAS C. SKALAK, AND GEERT W. SCHMID-SCH~NBEIN

AMES-Bioengineering,

University of California, San Diego, La Jolla, California 92093 Received November 10, 1983

A quantitative analysis of blood flow dynamics in skeletal muscle requires a detailed picture of the microvascular network. This report presents an analysis of the arteriolar network structure in the spinotrapezius muscle of the rat. The microvasculature is visualized by injection of a carbon suspension and recorded in the form of photomicrographs with a complete reconstruction of the microvasculature on transparent overlays. The spinotrapezius muscle has several major feeding arterioles which supply blood into an extensive meshwork of interconnecting or arcading arterioles spanning the entire muscle. The connections from the arcade arterioles to the capillaries are provided by transverse arterioles, which branch from the arcades at regular intervals. Each transverse arteriole forms a single asymmetric dichotomous tree and within each muscle there is a wide range in the size of transverse arterioles. A new branching schema is proposed to describe the arteriolar network. A set of network parameters is derived and typical values of these parameters in the spinotrapezius muscle of the rat are provided. Q 1985 Academic press. IIIC.

INTRODUCTION One of the key requirements to develop quantitative descriptions of microvascular blood flow is a detailed analysis of the vessel geometry and network branching pattern. Although general features of the microvasculature in skeletal muscle have been described almost a century ago (Spalteholz, 1888),the current descriptions are sketchy and largely concerned with the capillary network (see reviews by Walls, l%O; Wiedemann, 1963; Hammersen, 1968; Hudlicka, 1973; Baez, 1977). Qualitative descriptions of the arteriolar or venous network in skeletal muscle are available (Spalteholz, 1888; Blomfteld, 1945; Zweifach and Metz, 1955; Grant, 1964; Stingl, 1969; Erikson and Myrhage, 1972; Myrhage, 1977). In the face of the importance of microvascular anatomy as a basis for understanding mass and heat transport in skeletal muscle, it is necessary to consider this subject anew from a quantitative point of view. In this report we will describe the arteriolar network. Descriptions of the capillary and venous network will be given in separate publications. For any skeletal muscle, the artery-arteriolar network may be conveniently divided into two parts: (A) An arteriolar network inside the muscle, (B) an array of small ’ This work is supported by NSF Grant PCM-8215607. We thank Frank DeLano and Gary Firestone for their assistance in the muscle preparations and Peme Whaley for her excellent typing of the manuscript. 29 CKm-2sms5 $3.00 Copyright 0 1985 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in U.S.A.

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ENGELSON,

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AND SCHMID-SCHbNBEIN

arterial vessels that supply blood to the muscle as branches from central arteries. These latter vessels are located outside the muscles in connective tissue and are designated as feeding arteries or arterioles. The distinction between the term artery and arteriole is only a matter of vessel size: arterioles are less than about 100 pm in diameter, arteries are larger. Early reports from intravital studies of skeletal muscles in experimental animals and from histological studies in man have shown the presence of several feeding arterioles (Blomfield, 1945; Hudlicka, 1973), so that occlusion of one of the feeding arterioles does not necessarily interrupt blood flow in the capillary network. For example, in a muscle such as the spinotrapezius muscle of the rat, the entire capillary network continues to be perfused even when two out of approximately three major feeding arterioles are tied off. This is a remarkable phenomenon. The question arises, how is the flow redistribution achieved? The answer lies in the specialized arrangement of the arterioles embedded in the muscle. There exists a meshwork of interconnected arterioles which have been designated as arcade arterioles (Zweifach and Metz, 1955)or as arteriolar macro- and micromesh (Saunders et al., 1957). These arcade arterioles have important hemodynamic consequences with respect to organ perfusion. We have observed them in the tenuissimus muscle of the cat, and the cremaster, gracilis, and spinotrapezius muscles of the rat. They have also been described in connection with modules in the mesentery of the cat (Frasher and Wayland, 1972). The arcade arterioles are connected to the capillaries through a set of smaller arteriolar branches which we designate as transverse arterioles. It is obvious that the arteriolar network cannot be regarded as a dichotomously branching tree such as the pulmonary airways (Weibel, 1963). In the following text a new branching schema will be introduced and then a detailed arteriolar network description in the spinotrapezius muscle of the rat will be provided. Values will be listed for network parameters from carboninfused muscle specimens. METHODS (a) Animal Preparation Wistar-Kyoto rats (Charles River Breeders) at 16-20 weeks of age and with average weight of about 350-360 g were used. General anesthesia was induced with a mixture of 1% chloralose and 13.3% urethane (0.6 ml/l00 g im) in accordance with the university regulations for animal welfare. Body temperature was kept at 37°C with a heating pad at all times. The femoral artery and vein were each catheterized with PE-50 catheter tubing. In one group of animals, the spinotrapezius muscle was exteriorized according to the procedure by Gray (1973). About 5 silk sutures (6-O) were inserted along the edge of the muscle to allow it to be stretched to approximately the in vivo length. The muscle was suffused with a balanced Krebs solution at 35°C which was maintained at pH 7.4 by a bicarbonate CO, buffer with continuous CO* bubbling. In a separate group of animals, the spinotrapezius muscle was not exteriorized for microscopy but instead was only exposed through a skin incision and removal of the fascia and white adipose tissue. By this means, all feeding arterioles to the muscle were kept intact. In general, the less dissection was carried out the better the carbon filling.

ARTERIOLAR

NETWORK

IN

MUSCLE

31

(b) Filling of Microvessels with Carbon and Tissue Preparation Dibenzyline (Smith, Kline and French Labs., Philadelphia) was administered through the femoral venous catheter (1.Omg/kg body wt) to prevent vasoconstriction during the carbon exchange. To obtain uniform filling of the microvasculature by carbon, blood was first isovolumetrically replaced with heparinized saline (10 units/l0 ml saline) containing dibenzyline (10 pg/lml saline) and bovine serum albumin (0.25 g/100 ml). Otherwise coagulation is initiated when the ink particles come into contact with whole blood (even in the presence of heparin), resulting in a patchy and incomplete filling of the microvasculature. Additional booster injections of anesthesia were given during the blood exchange. A single dose of Nitroprusside (10 pg/ml) was topically applied to the spinotrapezius muscle. Perfusion through the femoral artery was continued for about 5 min until the majority of red cells were removed. The perfusion pressure was kept at about 100 mm Hg and monitored with a mercury manometer. The infusion solution was then immediately switched to filtered India ink (Pelican Drawing Ink, Gunther Wagner Pelikan-Werke, West Germany). The femoral venous outflow was stopped when the majority of the capillaries were filled with carbon (after about 5 min). Under such conditions the arterioles and venules were also uniformly filled. At this stage the arterioles were dilated. Thereafter, the suffusate was replaced by a fixative (l/2% glutaraldehyde in saline adjusted with distilled water to 300 mOsm, pH 7.4, by addition of NaOH) for 15 min, followed by 1% glutaraldehyde (300 mOsm, pH 7.4) for 15 min. Then the muscle was postfixed in situ with 30, 50, 70, and 100% AFC solution (87% ethanol, 10% formaldehyde, 3% glacial acetic acid; dilutions in distilled water) for 15 min at each increment. The ink infusion pressure was maintained at 100mm Hg during the glutaraldehyde and AFC fixation periods. The muscle was excised and placed on a petri dish with the silk sutures embedded into a perimeter of molding clay to maintain a flat specimen. The 100% AFC solution was exchanged several times over a period of 4-6 hr and was then replaced by 100% glycerine to clear the muscle. We found methyl salicylate to be a more effective clearing agent for nonexteriorized muscles. These specimens were left in situ in the thoracic wall after carbon filling and fixation. Then the entire spinotrapezius muscle and adjacent muscles and connective tissue were excised and cleared. This procedure allowed us to locate the major feeding arteries and arterioles supplying the spinotrapezius muscle (Fig. 1). In cleared specimens the ink-filled vessels stand out as dark structures against a light background. Wherever possible, remaining fascia and adipose tissue were carefully trimmed away under a dissecting microscope. The exteriorized specimens in glycerine were sandwiched between two microscope slides (25 x 50 mm) held together by a thin perimeter of modeling clay or silicone sealer. Care was taken not to compress the muscle because compression of blood vessels displaced the carbon and left segments or whole vessels unmarked. The specimens in methyl salicylate were stored in glass containers and viewed in flat glass petri dishes. (c) Photography and Network Reconstruction (i) Feeding and arcade arterioles. The entire muscle was photographed with a 35-mm camera (Kodak, Technical Pan Film 2415) through a Leitz intravital

32

ENGELSON,

SKALAK,

AND

SCHMID-SCHONBEIN

FIG, 1. Microphotographic montage of a carbon-filled microvasculature in the spinotrapezius muscle of the rat. In the line drawing (bottom) the feeding and arcade arterioles are reproduced. The connections to the transverse arterioles as well as capillaries and venules are not shown for the sake of clarity. Diameters are not drawn to scale. The orientation of the muscle is as follows: right side, anterior end; left side, posterior end; top, lateral side; bottom, medial side along the spine. The three arrows indicate the feeding arterioles to the muscle. The feeder at the right is a branch from the brachiocephalic artery, the feeder at the top left connects to the 11th intercostal artery, and the feeder at the bottom connects to an arcade artery in the underlying latissimus dorsi muscle and to the 10th intercostal artery.

microscope under transillumination with a 3.5 x objective and 10x eyepiece ocular. Individual 3 x 5-in. prints were assembled into a montage of the muscle microvasculature. Approximately 20 prints were required to assemble a network. The exact magnification was established by photography of a 2-mm microscale (lo-pm division, American Optics) under identical conditions as the muscle specimen. The arterioles were traced by hand on a transparent overlay on the photomontage. Although the majority of feeding and arcade arterioles are situated in the plane of the spinotrapezius muscle, they are not all simultaneously in focus on the photomontage. Therefore, frequent comparisons of the specimen through the

ARTERIOLAR

NETWORK

IN

MUSCLE

33

microscope was a necessary adjunct to tracing the entire arteriolar network. In this way all arteriolar connections in the muscle from branch point to branch point were identified. If a muscle specimen contained incompletely filled arterioles, i.e., without complete connection from one bifurcation to another, that section was excluded from further analysis. (ii) Transverse arterioles. Photography and reconstruction of transverse arterioles was performed in the same way as for the arcades, except that a 20 x objective was used. Arterioles were selected for analysis only when the entire tree could be observed. The essential requirement in this respect was that all capillaries supplied by a transverse arteriole had to contain carbon. Almost all of the arterioles analyzed were located in the thin regions of the muscle so that no bifurcation was obscured by overlying or underlying vessels. Otherwise the transverse arterioles were selected at random without preference for size or other characteristics. The lurninal diameters of the carbon-filled blood vessels were measured manually with the image shearing device (Intaglietta and Tompkins, 1972) with a 20x objective. The uncertainty in this measurement is of the order of 0.4 pm as seen by the maximum deviation of repeated measurements on a single vessel. The individual vessels comprising the arcades and transverse arterioles exhibit no taper within resolution of light microscopy. Changes in diameter occur only at branchpoints. Therefore a single luminal diameter measurement was used to characterize a given vessel.

(d) Data Analysis In order to explain the choice of network parameters to be measured, it is necessary to briefly describe the arteriolar network. Figure 1 shows a photograph and its corresponding line drawing of the feeding and arcading arterioles in the spinotrapezius muscle. For clarity, the transverse arterioles are not shown, but in Fig. 2 a smaller segment of arcade arterioles is shown with simplified representations of transverse arterioles. From the micrographs, it is apparent that the muscle has several feeding arterioles which connect to form a meshwork of arcading arterioles. The connections to the capillaries are provided by transverse arterioles which arise from the arcade arterioles at regular intervals. Figures 3a, b, show two examples of transverse arterioles. The distal portions of the transverse arterioles feed directly into the capillaries. The point of transition between transverse arterioles and capillaries was identified by the following criteria: capillaries are terminal branches of transverse arterioles which are usually thinner than the parent (order 2) vessels, and which travel parallel to the muscle fibers. We find that the transition from the transverse arterioles to the capillaries occurs at points where many capillaries are arrayed in the parallel alignment that is so characteristic for skeletal muscle. This transition point also corresponds to the last appearance of vascular smooth muscle along the transverse arterioles, according to our current histological studies (Skalak et al., 1982). The transverse arterioles are asymmetric bifurcating trees without direct anastomoses, whereas the arcade arterioles form a meshwork. Their functions may be quite different and they need to be described separately. (i) Bifurcation pattern of feeding and arcade arterioles. The schematic shown in Fig. 4 depicts an arcading network with several feeding vessels, but with the

34

ENGELSON,

SKALAK,

AND SCHMID-SCHSNBEIN

FIG. 2. Microphotographic montage of a carbon-filled microvasculature in the spinotrapezius muscle of the rat. In the line drawing (bottom), arcade arterioles together with the transverse arteriolar branches are reproduced. Diameters are not drawn to scale. The transverse arterioles are reproduced incompletely. For a complete display of some of these trees see Fig. 3.

transverse arterioles omitted for clarity. We will assume that the meshwork is planar, i.e., no crossing of arcading vessels occurs in the plane, and that the meshwork spans over a skeletal muscle tissue with volume V. Any point where three vessels form a junction will be referred to as a node. In Table 1, a list of seven parameters is given which describe the arcade meshwork. They are expressed in Table 1 as absolute numbers without reference to the muscle volume V. For comparison with other skeletal muscles and among different rat species it is desirable to express the same set of parameters normalized with respect to V. These normalized quantities will be designated with capital letters. For example, let nF be the number of feeder vessels in a muscle, then NF = nF/V is the number of feeder arterioles per volume of muscle tissue, N’ = d/V is the number of internal nodes per unit volume, etc. NF includes the feeders that enter along the perimeter of the arcades as well as feeders connecting into the interior of the arcade meshwork. Such internal feeders are occasionally observed in the

ARTERIOLAR

a

NETWORK

ZN MUSCLE

35

b

FIG, 3. Microphotographic montage of a small (a) and large (b) transverse arteriole in the spinotrapezius muscle of the rat. The line drawing (middle) shows a reconstruction of the vessel made by comparison with the original specimen and the bottom drawing shows a schematic of the branching pattern. (a) Shows the branching order numbers according to the Strahler technique.

36

ENGELSON,

P-5

SKALAK,

np-5

AND

SCHMID-SCHiiNBEIN

k-5

FIG. 4. Schematic of a hypothetical arcade network. For explanation of symbols see text and Table 1.

spinotrapezius muscle, although none are present in the specimen shown in Fig. 1. Of the seven parameters that describe average meshwork properties, only three are independent. The remaining four are related by the following equations. The total number of nodes N in the arcade arteriolar network (disregarding the transverse arterioles) is N = N’ + Np + NF.

(1)

There are K individual arcade loops per unit volume in the meshwork, and for a planar meshwork with bifurcations K = (1/2)(Np + N’) + l/V.

(2)

The reader can easily verify this relationship, e.g., by inspection of Fig. 4. If there are N* number of individual arterioles per unit volume, excluding the feeding vessels, then for a network with bifurcations N* = (1/2)(3N - NF).

(3)

This equation can also be easily verified. It is derived from the condition that three vessels join to each node (3N) and that the total number of nodes consists of two for each vessel (2N*) plus the nodes to the feeders (NF). By substituting Eqs. (1) and (2) into (3), we find the identity NF + 3K = NA + 3/V.

(4)

Furthermore, we note that for a dichotomous arcade network the average number of vessels around a single arcade m* is m* = [2(N* - NF - N? + NF + NT/K. TABLE 1 ARCADE ARTERIOLES NETWORK

nF np nr n k

mA nA

PARAMETER

Number of feeder arterioles Number of bifurcations along the arcade perimeter Number of bifurcations inside the arcade meshwork Total number of nodes in the arcade meshwork Number of arcades in the meshwork Number of arterioles per arcade Number of arterioles in the arcade meshwork (excluding feeder arterioles)

(5)

ARTERIOLAR

NETWORK

IN MUSCLE

37

N* - NF - Np is the number of vessels in the interior of the arcades (disregarding the transverse arterioles) and NF + Np is the number of vessels along the arcade p&meter. mA is a number greater than 1 because at least two vessels are needed to form an arcade loop. It can be shown (Smith, 1954) that with increasing size of the arcade network in the presence of dichotomies lim m* = 6 N+m A large arcading network will have, on the average, six vessels around each arcade loop, i.e., a hexagonal pattern. Typical values in the spinotrapezius muscle fall between 5 and 6. Solving Eq. (5) for N*, we find N* = 1/2(m* * K + NF + NT.

(6)

We see from Eqs. (1) through (6) that by measuring three parameters, e.g., NF, Np, and N’, the network arrangement of the arcades in terms of N, K, N* and m* is completely specified. The use of these equations permits any set of three parameters to be used to compute the remaining four. Experimentally, we find that a convenient set of parameters to measure is NF, K, and m*, but other parameters can also easily be measured from the photomontages. Let e be the total length of the arcading arterioles in a volume V so that L = e/V is the length of arcades per unit volume. The mean length of single arterioles in the arcade network is 1 = e/n* = L/NA.

(7)

L can be measured conveniently by means of a stereological technique (SchmidSchiinbein et al., 1977) using a test grid system according to L = LA/h, where LA is the length of the arcade vessels per unit planar area. h is the average thickness, which was measured by cutting each muscle in the observation area at right angles to the fibers at three to four locations. Along each cut, about 30 to 40 thickness measurements were taken at a spacing of 190 pm, and the individual measurements were averaged for each muscle. The thickness of a muscle in the center portion was relatively constant, but there was usually some taper toward the edges. (ii) Bifurcation pattern of transverse arterioles. Transverse arterioles, by definition, originate with single trunks at regular intervals along the arcade arterioles, and terminate with the capillaries. They form asymmetric dichotomous branching trees of variable size (Figs. 3a, b). To find the average spacing, z, between transverse arterioles we measured their separation along about 20 arcading arterioles. To reconstruct the tree structure, each transverse arteriole was first traced and represented as a schematic diagram (Fig. 3a, b; bottom graph) to show its branching pattern, Such asymmetric trees can be described either in a forward mode, as proposed for the airways (Weibel, 1963), or in a retrograde mode as used for trees and rivers (Strahler, 1952; Fenton and Zweifach, 1981). In the Strahler technique, capillaries are regarded as generation 1. Wherever two vessels of order 1 join, an order 2 is formed, etc. If two vessels of unequal order join,

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ENGELSON,

SKALAK,

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SCHMID-SCHiiNBEIN

the higher order is continued in the parent vessel. Using such a schema, the number of vessels, ZV,, in order 12is computed from the number of capillaries, Ni, according to (Strahler, 1952): N,, = R;-n N,, where RB is the branching order number

where I is the highest order in the tree. Vessel length and diameter were described with a slightly modified version of the Strahler technique. The length, L,, and diameter, D,, of vessels in order n is computed from the length, L2, and diameter, D2, respectively, of the second order vessels. Since the length ratio, RL, and the diameter ratio, RD, are independent of capillary lengths and diameters, respectively, IZ must be greater than 1 when calculating L, or D, L, = R;-2 L2

(10)

where RL =

(11)

D, and R,, are computed according to Eqs. (10) and (11) by replacing L; with Di. This modified scheme gives a better approximation to the geometry of transverse arterioles than the original Strahler technique. RESULTS In the following, we will list values for geometric and topological parameters of the arteriolar network as obtained in a typical spinotrapezius muscle from a Wistar-Kyoto rat. These values are representative for a group of nine muscles that have been investigated in detail. It should be recognized that there are differences among strains. In an upcoming publication, a comparison of these parameters will be provided between Wistar Kyoto and spontaneously hypertensive rats. All arteriolar blood vessels in both rat species could be analyzed by the scheme proposed above. The arcade arterioles connect to the arcade venules via the transverse arterioles, the capillaries, and the collecting venules. We observed no direct arteriovenous anastomoses. Feeding and Arcade Arterioles Table 2 lists arcade parameters as measured in a typical spinotrapezius muscle (Fig. 1) of a mature animal. All network parameters are indicated in absolute numbers for the single muscle. They can be readily converted to normalized quantities by dividing by the volume V. There are three feeding vessels with a relatively wide distribution of diameters, indicating that there exist small and large feeders. There are typically K = 0.235 arcade loops per cubic millimeter of muscle volume V which, at a typical value of V = 115 mm3 for mature

39

ARTERIOLAR NETWORK IN MUSCLE TABLE 2 Topo~oov

OF FEEDING

AND ARCADE ARTERIOLES IN SPINOTRAPEZIUS

V = 115 mm3 nF = 3 D = 81.0 pm mA= 5.1 d = 30 np = 22 n = 55 nA = 81

Muscle volume Number of feeding arterioles to the muscle Mean luminal diameter of feeding arterioles Number of arterioles per arcade loop Number of internal nodes Number of peripheral nodes Number of nodes Number of arcade arterioles Number of arcades Length of arcades per unit volume Mean length of arcade arterioles (81 vessels) Mean

luminal

diameter

of arcade

arterioles

MUSCLE

(81 vessels)

Average spacing between transverse arterioles

k

=27

L L B 2

= = = =

1.17 mm/mm’ 1660pm 43.3 pm 190 pm

animals, amounts to 27 arcade loops for this muscle. Mean arcade arteriolar length and diameter values are indicated in Table 2, and their frequency distributions will be presented in the upcoming paper.

Transverse Arterioles The use of the Strahler technique to quantify the branching topology and vessel geometry of given vessel orders is illustrated in Table 3. Observed and predicted values are shown for the number of branches, mean diameter, and mean length of each vessel order for the two transverse arterioles of Figs. 3a, b. The largest error occurred in making predictions of length values. It is not unusual for one of the higher orders (e.g., order 4 at the bottom of Table 3) to have an average length which exceeds the average length of both a higher and a lower order. These unusually large branches invariably connect to capillary networks which are remote from the arcade arteriole where the transverse arteriole originated. In large transverse arterioles the highest order vessel length is occasionally less TABLE 3 PREDICTION

OF TRANSVERSE ARTERIOLE

TOPOLOGY BY STRAHLER TECHNIQUE

No. of branches per order

Transverse arteriole of Fig. 3a

Transverse Arteriole of Fig. 3b

Order

Observed

Predicted

1 2 3 4

16

(16)

6

6.3 2.4 1.0

R,, = 2.56

1 2 3 4 5

2 1

Observed

Predicted

R, = 1.64

RB = 2.92 65 (65)

25 7 2 1

Mean diameter for each order (pm)

22.3 7.6 2.6 0.9

5.4 6.6 13.5

(5.4) 8.7 14.3 RD = 1.38

5.4 6.6 8.9 14.0

(5.4) 7.5 10.3 14.2

Mean length for each order (pm) Observed

Predicted

R, = 1.33

123.8 153.0 219.0

(123.8) 164.7 219.0 RL = 1.32

92.6 168.3 337.0 95.0

(92.6) 126.9 173.8 238.1

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ENGELSON,

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SCHMID-SCHGNBEIN

than the length of the next lower order, which also contributes to the discrepancy between observed and predicted lengths. The length of some of these orders may only be predicted with the Strahler technique within a factor of 2, but the majority of predictions of number of branches, diameter, and length is usually within an error of about 10%. DISCUSSION The network schema proposed in this paper for arterioles in skeletal muscle gives a comprehensive characterization of network topology and vessel geometry. There are two motives for such a characterization: the geometric and topological parameters are essential for a quantitative analysis of microvascular blood flow in this organ, and these parameters are needed for a detailed comparison of healthy and diseased animals. In an upcoming publication, a comparison is provided between normotensive and hypertensive animals. This comparison shows that no single parameter by itself is sufficient for a meaningful comparison of the two networks in such animals. Rather a family of parameters is required to compare anatomical alterations. It should be recognized that distinct differences in the arteriolar network are found among different strains of rats. The values of the network parameters listed in Tables 2 and 3 are to be taken as typical only for the spinotrapezius muscle. Microvascular Network Topology The separation of the network into arcading arterioles and feeding arterioles is a natural schema suggested by the anatomical arrangement of the vessels. The transverse arterioles form asymmetric trees which are well described by the Strahler formalism. It is possible, by measurement of the number of vessel orders, branch ratio (&), diameter ratio (R,), and vessel length ratio (RL), to achieve a complete characterization of the transverse arterioles. The arcade arterioles do not exhibit such a tree-like configuration. Theirs is a meshwork configuration. In addition to vessel geometry, important parameters in such an arcade system are the number of feeding arterioles (NF), the number of arcade loops (K), and the number of vessels forming each arcade loop (m*). As shown by the identities in Eqs. (1) to (6), other topological parameters which characterize the arcade meshwork can be computed from these three independent measurements. The distinction made between transverse and arcade arterioles should not be interpreted as indicative of a functional correlation, e.g., with respect to innervation, without further experimentation. The network schema and its parameter characterization account for average anatomical parameters. With this schema, it is possible to reconstruct vascular models with an arrangement of feeding, arcade, and transverse arterioles which have the same parameters as described for an animal specimen. Although average network features may be accurately reproduced in this way, the precise pattern of vessel connections is not duplicated. For such detail a larger number of network parameters would be required, such as the conductance matrix in a linear hemodynamic network computation (Lipowsky and Zweifach, 1974), or the method with Bra and Ket operators proposed by Chen and Prewitt (1982).

ARTERIOLAR

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IN

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41

The Function of Feeding and Arcade Arterioles The presence of an arcading arteriolar network on the level of the microcirculation is a striking fact that has received little emphasis. Quite likely, the arcading arrangement has an impact on many different functions which are only little known at this time. It is relevant here to briefly discuss three implications. The arcade arterioles cover a relatively large tissue area (in the spinotrapezius muscle of the rat it is about 7-10 cm2). The existence of as many as three to four large feeding arterioles supplying blood to a given mass of tissue creates a problem with respect to distributing the blood uniformly to the array of capillaries. These feeding arterioles are branches of the brachiocephalic artery and several intercostal arteries (Fig. 1). Intravital microscopic measurements of pressure and flow in the same arcade arterioles (Zweifach et al., 1981) show relatively small pressure gradients throughout the arcades. A much steeper pressure gradient exists across the transverse arterioles. Frequently, one also observes reversal of flow in the arcade arterioles, a further indication of the existence of small pressure gradients. Thus, one of the functions of the arcades may be to maintain the hydrostatic pressure within a relatively uniform range over the entire extent of the muscle so that the hydrostatic pressure at the entrance to the transverse arterioles is kept uniform throughout the muscle. Early workers recognized that following injury to muscle (e.g., by a bullet penetration) only the contiguous tissue along the path of the injury becomes necrotic, whereas the remainder of the injured muscle may survive and remain well perfused (Blomfield, 1945). This feature of muscle is in line with the presence of multiple feeding arteries and the existence of arcades which ensure that any capillary group may be supplied with blood through several different arteriolar pathways. If one pathway is interrupted through injury, compression of the tissues, or other causes, blood flow may still be maintained to the capillaries through collateral pathways. Gannon et al. (1983) have also shown that in the arcade arterioles of the mesentery, a reduction of perfusion pressure has only a relatively minor effect on the flow distribution in the arcade network. The majority of arterioles in the muscle demonstrate spontaneous vasomotion in the form of periodic smooth muscle contractions (Borders, 1980). They also undergo small elastic distensions in response to the pulsatile arteriolar pressure. In a recent investigation, we have shown that the terminal lymphatics in skeletal muscle are located in immediate proximity to the arcading arterioles. Although the lymphatics have no smooth muscle of their own, volume changes in the lymphatics are induced by corresponding arcade arteriolar volume changes. For example, if arcade arterioles are completely relaxed, the adjacent lymphatics are compressed whereas if the arterioles are contracted, the lymphatics are open (Skalak et al., 1984, 1985). Thus, by vasomotion and elastic pulsatile distensions, arcade arterioles in skeletal muscle also serve as the pump mechanism for lymph formation and thus tissue filtration. Very few transverse arterioles and no capillaries are accompanied by lymphatics. The Function of Transverse Arterioles The transverse arterioles are also regularly observed to undergo extensive vasomotor excursions in the living preparation. The diameter values that we

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SKALAK,

AND SCHMID-SCHiiNBEIN

have listed above should be regarded as indicative of the vasodilated state. Transverse arterioles in the contracted state frequently obliterate their lumen so that blood flow stops entirely. As a consequence of their strategic location at the entrance to the capillaries, their contraction leads to simultaneous cessation of blood flow in the distally connected capillary bed. Thus, each transverse arteriole has a powerful but localized influence on capillary perfusion. Tissue Fixation A primary concern in measurements made on tissues prepared with chemical fixatives is the possibility of cell and vessel distortion. Chemical fixation is associated with the conversion of a viscoelastic material into an elastic gel. On one hand, tissue distortion may arise as a result of the osmotic force exerted by the conventional fixatives, such as 0~0~ or glutaraldehyde. On the other hand, composite tissues such as muscle may contain components such as elastin which are incompletely fixed and continue to distort the tissue after fixation over longer periods of time. This latter problem was found to be particularly serious in the lung and has been investigated by Sobin et ai. (1981). In skeletal muscle, the latter problem appears to be less serious. Observation of the vasculature in a fixed muscle over several days following the primary fixation with glutaraldehyde shows no dimensional changes within resolution of light microscopy. This may be due to strong mechanical support by the fixed muscle fibers. Investigating the diameter of a single vessel during fixation with AFC solution gave the following results. The vessel diameter after vasodilation was 56 pm with uncertainty of ? 3 pm, and was reduced to 53.2 pm after filling with carbon, fixation, and clearing with glycerine. These results indicate that vascular dimensions in vivo and after carbon filling agree within experimental error of the in vivo diameters. This observation on a single vessel is also supported by observation of vessel populations. For example, the average diameter of the highest order of the transverse arterioles at the point where they connect to the arcade arterioles was measured in Wistar-Kyoto rats as 20.4 ? 9.0 (SD) pm (Zweifach et al., 1981) and was found in this study to be 18.6 + 7.0 pm. This difference is statistically not significant and is possibly not related to the fixation but to the reduced light diffraction in the glycerine-cleared specimen. Arteriolar Cross Sections The present values for diameters refer only to the vasodilated states due to treatment with a vasodilator at a transmural pressure of 100 mm Hg. Under these conditions we find no evidence for taper along the length of the arterioles in support of the report by Sobin and Tremer (1980). This includes sites in the first order of the transverse arterioles where precapillary sphincters have been seen previously. Vessels in the vasodilated state show a change in their dimensions only at bifurcations. Histological sections further indicate that the cross sections of all dilated arterioles closely approximate a circle. However, during vasoconstriction (e.g., with topically applied norepinephrine), the cross-sectional configuration of the arterioles is changed by folding of the endothelial cells to the extreme that in strongly contracted vessels, the lumen may be completely obliterated. Under these conditions the notion of “vessel diameter” is untenable

ARTERIOLAR

NETWORK

IN

MUSCLE

43

because the lumen cross section has no resemblance to a circle (Van Citters, 1966). Under normal physiological conditions in the presence of vascular tone, we frequently observe small changes of the diameter in the first or second order vessels of the transverse arterioles. These sites are usually referred to as precapillary sphincters. A narrow portion may be present along a variable length at the entry region to the capillaries. This then typically widens (by 1-2 pm) to the dimension of the capillaries. Except for occasional small intrusions of the lumen by endothelial nuclei, capillary diameters remain constant at normal transmural pressures. Application to Other Muscles The present arteriolar network scheme may be applied to other muscles. Preliminary investigations of the network structure in the rat gracilis and cremaster muscle also show several feeding arterioles and an arcade meshwork with regularly spaced transverse arterioles. A similar arrangement exists in the mesentery of the cat (Frasher and Wayland, 1972) and in human muscle (Saunders et al., 1957), but currently no quantitative details are available. The advantage of the spinotrapezius muscle is that the entire network can be visualized in a carbonfilled, planar specimen. In thicker muscles, a different approach for visualization of the microvasculature needs to be designed so that quantitative network analysis can proceed. REFERENCES S. (1977). Skeletal muscle and gastrointestinal microvascular morphology. In “Microcirculation” (G. Kaley, B. M. Altura, eds.), Ch. 3, pp. 69-94. Univ. Park Press, Baltimore. BLOML~ELD, L. B. (1945). Intramuscular vascular patterns in man. Proc. R. Sot. Med. 38, 617-618. BORDERS, J. (1980). “Vasomotion Patterns in Skeletal Muscle in Normal and Hypertensive Rats.” Ph.D. dissertation, University of California, San Diego. CHEN, I. I. H. AND PREWITT,R. L. (1982). A mathematical representation for vessel network. J. Theor. Biol. 97, 211-219. ERIKSSON, E., AND MYRHAGE,R. (1972). Microvascular dimensions and blood flow in skeletal muscle. Acta Physiol. Stand. 86, 211-222. FENTON,B. M., AND ZWEIFACH,B. W. (1981). Microcirculatory model relating geometrical variation to changes in pressure and flow rate. Ann. Biomed. Eng. 9, 303-321. FRASHER, W. G., AND WAYLAND, H. (1972). A repeating modular organization of the microcirculation of cat mesentery. Microvasc. Res. 4, 62-76. GANNON, B. J., ROSENBERGER, S. M., VERSLUIS,T. D., AND JOHNSON, P. C. (1983). Autoregulatory patterns in the arteriolar network of cat mesentery. Microvasc. Res. 26, l-14. GRANT, R. T. (1964). Direct observation of skeletal muscle blood vessels (rat cremaster). J. Physiol. (London) 172, 123-137. GRAY, S. D. (1973). Rat spinotrapezius muscle preparation for microscopic observation of the terminal vascular bed. Microvasc. Res. 5, 395-400. HAMMERSEN, F. (1968). The pattern of the terminal vascular bed and the ultrastructure of capillaries in skeletal muscle. In “Oxygen Transport In Blood and Tissue” (D-W. Lubbers, U. C. Luft, G. Thews, E. Witzleb, eds.), pp. 184-197. G. Thieme Verlag, Stuttgart. HUDLICK;, 0. (1973). “Muscle Blood Flow. Its Relation to Muscle Metabolism and Function.” Swets and Zeitlinger, B. V., Amsterdam. INTAGLIETTA, M., AND TOMPKINS, W. R. (1972). On-line measurements of microvascular dimensions by television microscopy. J. Appl. Physiol. 32, 546-551. LIPOWSKY, H. H., AND ZWEIFACH, B. W. (1974). Network analysis of microcirculation of cat mesentery. Microvasc. Res. 7. 73-88. BAEZ,

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MYRHAGE,R. (1977). Microvascular supply of skeletal muscle fibers. Acm Orthop. &and. Supp[. 168, 1977.

R. L. DEC. H., LAWRENCE, E. J., MACIVER, D. A., AND NEMETHY, N. (1957). The anatomical basis of the peripheral circulation in man. On the concept of the macromesh and micromesh as illustrated by the blood supply of muscle in man. In “Peripheral Circulation in Health and Disease” (W. Redish, F. F. Tango, R. L. de C. H. Saunders, eds.), Grune & Stratton, New York. SCHMU&%NBEIN, G. W., ZWEIFACH, B. W., AND KOVALCHECK, S. (1977).The application of stereological principles to morphometry of the microcirculation in different tissues. Microvasc. Res. 14, 303SAUNDERS,

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C., SCHMID-SCH~NBEIN, G. W., ANDZWEIFACH, B. W. (1982).Topological and morphological studies of the microvascular network in rat spinotrapezius muscle. Znr. J. Microcirc. 1, 321-322. SKALAK, T. C., SCHMID-SCH~NBEIN, G. W., AND ZWEIFACH, B. W. (1984). New morphological evidence for a mechanism of lymph formation in skeletal muscle. Microvasc. Res. 8, 95-112. SKALAK, T. C., SCHMID-SCH~NBEIN, G. W., AND ZWEIFACH, B. W. (1985). Lymph transport in skeletal muscle. In “Tissue Nutrition and Viability.” (A. R. Hargens, ed.), Springer-Verlag (in press). SMITH, C. S. (1954). The shape of things. Sci. Amer. 190, 58-64. SOBIN, S.S., FUNG, Y. C., AND TREMER,H. M. (1981). The effect of incomplete fixation of elastin on the appearance of pulmonary alveoli. J. Biomech. Eng. 104, 68-71. SOBIN, S. S., AND TREMER,H. M. (1980). Cylindricity of the arterial tree in the dog and cat. Fed. Proc. 39(II), 269. SPALTEHOLZ,W. (1888). Die Verteilung der Blutgefasse im Muskel. Abh. Siichs. Ges. Wiss. Math. Phys. Kl. 14, 509-528. STINGL,J. (1969). Arrangement of the vascular bed in the skeletal muscles of the rabbit. Fol. Morphol. SKALAK, T.

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STRAHLER,A. N. (1952). Hyposometric (area latitude) analysis of erosional topology. Bull. Geol. Sot. Amer. 63, 1117-l 142. VAN CITTERS, R. L. (1966). Occlusion of lumina in small arterioles during vasoconstriction. Circ. Res. 18, 199-204. WALLS, E. W. (1960). The micro-anatomy of muscle. In “Structure and Function of Muscle” (G. H. Boume, ed.), Vol. 1, pp. 21-61. Academic Press, New York. WEIBEL, E. (1963). “Morphometry of the Lung.” Academic Press, New York. WEIDEMAN, M. P. (1963). Patterns of arteriovenous pathways. In “Handbook of Physiology” (W. F. Hamilton and P. Dow, eds.) Section 2, Vol. 2, pp. 891-933. American Physiological Society, Washington, D.C. ZWEIFACH, B. W., KOVALCHECK, S., DELANO,F., ANDCHEN,P. (1981). Micro-pressure flow relationships in a skeletal muscle of spontaneously hypertensive rats. Hypertension 3, 601-614. ZWEIFACH, B. W., AND METZ, D. B. (1955). Selective distribution of blood through the terminal vascular bed of mesenteric structure and skeletal muscle. Angiology 6, 282-290.