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J Appl Physiol 82: 42-48, 1997;
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Journal of Applied Physiology
Vol. 82, No. 1, pp. 42-48, January 1997
EXERCISE AND MUSCLE

Alignment of microvascular units along skeletal muscle fibers of hamster retractor

Geoffrey G. Emerson and Steven S. Segal

The John B. Pierce Laboratory and Department of Chemical Engineering, Yale University, New Haven, Connecticut 06519

ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES


ABSTRACT

Emerson, Geoffrey G., and Steven S. Segal. Alignment of microvascular units along skeletal muscle fibers of hamster retractor. J. Appl. Physiol. 82(1): 42-48, 1997.---When muscle fibers contract, blood flow requirements increase along their entire length. However, the organization of capillary perfusion along muscle fibers is unclear. The microvascular unit (MVU) is defined as a terminal arteriole and the group of capillaries it supplies. We investigated whether neighboring MVUs along the fiber axis perfused the same group of muscle fibers by using the parallel-fibered retractor muscle. Hamsters were anesthetized and perfused with Microfil to visualize MVUs relative to muscle fibers. Fields of study, which encompassed five to seven neighboring MVUs along a muscle fiber, were chosen from the interior of muscles and along muscle edges. On average, MVUs were 1 mm in length, 0.50 mm in width, and 0.1 mm deep; segments of ~30 fibers were contained in this tissue volume of 0.05 mm3 (20 MVUs/mg muscle). The total distance across muscle fibers encompassed by a pair of MVUs is designated "union" (U); the fraction of this distance common to both MVUs is designated "intersection" (I). The ratio of I to U for the widths of neighboring MVUs provides an index of MVU alignment along muscle fibers (e.g., I/U = 1.0 indicates complete alignment, where the fibers perfused by one MVU are the same as those perfused by the neighboring MVU). We found that I/U along muscle edges (0.71 ± 0.02) was greater (P < 0.05) than the ratio measured within muscles (0.66 ± 0.02). A model predicted a maximum I/U of 0.58 with random MVU alignment. Thus measured values were closer to random than to complete alignment. These findings indicate that an increase in blood flow along muscle fibers requires the perfusion of many MVUs and imply that vasodilation is coordinated among the parent arterioles from which corresponding MVUs arise.

arteriole; capillary; functional unit; local flow control; microcirculation


INTRODUCTION

EXERCISE is the preeminent stimulus for increasing the activity of both skeletal muscle and the cardiovascular system. In response to exercise, blood flow to active muscles increases in proportion to the metabolic requirements of the respective muscle fibers (12, 15, 21). Indeed, the functional hyperemia and oxygen consumption of exercising muscle can exceed resting values by 50-fold (1, 12). The strong linear relationships among muscle work, oxygen consumption, and muscle blood flow manifested in humans (1), animals (12, 17), and isolated muscle preparations (15) imply a coupling between muscle fiber activity and microvascular perfusion. Nevertheless, a major gap exists in our understanding of how the controlled units of each system (i.e., muscle fibers and capillaries) interact with each other.

In skeletal muscle, a terminal arteriole (TA) gives rise to groups of 20-30 capillaries that run parallel to muscle fibers for a distance of ~1 mm (3, 6, 14). When a TA constricts or dilates, flow through all of its capillaries diminishes or increases, respectively (22, 23, 29). Because this functional unit is the smallest element of control for capillary perfusion in skeletal muscle (3, 6), it is referred to hereafter as a microvascular unit (MVU). This organization of capillary groups into MVUs is apparent in skeletal muscles from amphibians to primates (9, 10, 14, 19, 25, 28). TAs also control the flow of red blood cells into capillary groups in the saclike cremaster muscle (2, 22), which has a diverse orientation of both muscle fibers and capillaries.

The millimeter distance spanned by each MVU is considerably less than the length of skeletal muscle fibers, which often span many centimeters. Based on a compilation of histological and morphometric data, it was assumed that blood flow to the volume of muscle supplied by an MVU could be controlled independent of blood flow to the rest of the muscle (3). However, when a muscle fiber (or fiber group) contracts, it is metabolically active along its entire length and will require blood flow through the MVUs that supply corresponding segments of the fiber(s). The precision with which blood flow can be selectively controlled to a particular fiber (or fiber group; Ref. 4) will therefore depend on the alignment of the corresponding MVUs; if the MVUs encompass different fibers or fiber groups, there may be a mismatch between local requirements of muscle fibers and the capillaries actually perfused. This basis for blood flow heterogeneity (7) has not been previously examined.

In this study, we have used the parallel-fibered hamster retractor muscle (16, 20, 26) to test the hypothesis that the group of muscle fibers perfused by one MVU is the same group of fibers perfused by neighboring MVUs positioned along the muscle fibers. Our data shed new light on two fundamental questions. First, are MVUs aligned along the muscle fibers they supply? Second, is there a correspondence among the parent vessels that gives rise to MVUs that supply a muscle fiber or fiber group?


METHODS

All procedures were approved by the Animal Care and Use Committee of the John B. Pierce Laboratory and were performed in accord with the Guiding Principles in the Care and Use of Animals of the American Physiological Society.

Vascular casting. Male golden hamsters (n = 8, 106 ± 5 g; Charles River Breeding Laboratories) were anesthetized (pentobarbital sodium; 65 mg/kg ip). A tracheotomy was performed to ensure airway patency, and the left femoral vein was catheterized (PE-50) for infusing additional anesthetic (10-15 mg/kg) as needed. The abdominal aorta was cannulated retrogradely with PE-50 tubing, with the tip advanced just rostral to the diaphragm. The hamster was given an overdose of pentobarbital sodium intravenously, the vena cava was punctured for effluent, and 10 ml of Microfil casting compound (Flow-Tek) was infused into the abdominal catheter. The hamster was then stored at 4°C. Within 1-2 days after casting, retractor muscles were exposed and examined with a stereo microscope (model SV8, Zeiss) for uniformity of Microfil perfusion, and muscle length was measured from its caudal origin on the thoracic vertebrae to its rostral insertion on the cheek pouch (20). Muscles were carefully excised, trimmed of superficial connective tissue, pinned at in situ length in a petri dish coated with Sylgard (Dow Corning), and then stored at 4°C in 50% glycerin to preserve and clear the tissue (18).

Videomicroscopy. To highlight MVUs and arteriolar branches, retractor preparations were placed on the stage of an inverted microscope (Nikon Diaphot) and transilluminated with a 100-W halogen lamp (condenser numerical aperture, 0.52). Oblique epi-illumination from a 30-W fiber-optic lamp (Dolan-Jenner) highlighted the microvascular cast. Casts were examined at ×25 total magnification (×10 eyepieces; ×2.5/0.08 objective, Zeiss) to determine suitable areas of study (see Study fields). Then, with a ×4/0.13 objective (Nikon), images were focused onto a video camera (model IK-C30A CCD, Toshiba) coupled to a monochrome monitor (model PVM-122, Sony); total magnification on the monitor face was ×58. Video prints (model UP-870MD, Sony) were assembled to form a montage of the field under study. All measurements were calibrated with reference to stage micrometer (100 × 0.01 = 1 mm; Graticules).

Characterization of arterioles. Primary (1A) arterioles were designated as those segments that arose directly from feed arteries as they entered the muscle (16). Second-order (2A) arterioles typically run parallel to muscle fibers and serve as the principle distribution vessels. Branches from 2A arterioles were characterized as defined in RESULTS. Segment lengths between branches were measured along 2A and third-order (3A) arterioles (30) by using the eyepiece reticule; branch angles were measured with a protractor positioned on the video monitor (16).

Study fields. Each study field was 1 × 5 mm (width × length; Fig. 1); resolution of neighboring MVUs along the axis of a group of parallel muscle fibers was the principle criterion for field selection. Regions in which the Microfil casting was sparse were avoided, as were regions in which the casting was too dense to distinguish MVUs from each other. Each study field encompassed five to seven MVUs that intersected a 4-mm reference line oriented parallel to muscle fibers. On gross visual inspection, arteriolar network topology differed noticeably between the caudal and rostral regions of the muscle. Consequently, three study fields (from within the caudal, middle, and rostral one-third of muscle length) were selected for each of five muscles. To test for an effect of anatomic boundaries, study fields were also sampled along the edges of four additional muscles from respective regions. Each MVU in a study field was traced back to the 2A branch from which it originated.


Fig. 1. Analysis of microvascular unit (MVU) alignment in hamster retractor muscle. A: line drawing of excised retractor muscle pinned out in petri dish and filled with Microfil (as detailed in METHODS). FA, feed artery (2 FAs are shown giving rise to primary, second-order, and third-order arteriolar branches within muscle); O, muscle origin (caudal end) from spinous processes of last 3 thoracic vertebrae; I, muscle insertion (rostral end) on fascia of cheek pouch (20). Three 1 × 5-mm study fields are indicated by rectangles drawn in rostral, middle, and caudal regions of muscle; 2 fields are within muscle, 1 field is at muscle edge. B: boundaries of neighboring MVUs in study field. Dark 4-mm reference line is drawn parallel to muscle fibers (not shown for clarity) and capillaries and spans 5 MVUs. In practice, ratio of distance common to both MVUs in a pair ("intersection"; I) to total distance across muscle fibers encompassed by the pair ("union"; U) (I/U) was calculated for every pair of MVUs in field of study: primary (1°) pairs consist of adjacent MVUs (e.g., a and b, b and c, c and d, d and e); secondary (2°) pairs entail every other MVU (e.g., a and c, b and d, c and e); tertiary (3°) pairs are separated by 2 MVUs (e.g., a and d, b and e), and quaternary (4°) pairs are separated by 3 MVUs (e.g., a and e). In this example, there are four 1° pairs, three 2° pairs, two 3° pairs, and one 4° pair. C: boundaries of 1 MVU, as traced from middle MVU illustrated in Fig. 2A. Distance between upper (proximal) and lower (distal) boundaries indicates MVU width. TA, terminal arteriole from which capillaries in this MVU originate. D: I/U values for pairs of MVUs. U and I are indicated at left of each pair of rectangles (i.e., MVU boundaries). Bottom 2 examples illustrate how same I/U value (e.g., 0.5) may result from quite different physical relationships between neighboring MVUs.
[View Larger Version of this Image (24K GIF file)]

MVU perfusion fields. The boundaries of each MVU in the study field were measured at ×100 magnification (×10/0.25 objective, Zeiss) with reference to a reticule in the eyepiece. Boundaries were defined on the montage of the study field; focusing through the MVU ensured that the capillaries in each MVU were fully accounted for. Perpendicular to muscle fibers, the most proximal and distal capillaries originating from a TA defined MVU width; the caudal and rostral MVU boundaries were positioned coincident with the termination of Microfil in the capillaries (Fig. 1). Although the lack of complete filling facilitated the resolution of respective MVUs within a study field, it prevented resolution of the total distance spanned by the respective MVUs in vivo. Therefore, our measurement of MVU alignment is based on MVU width, which corresponds to the group of muscle fibers perfused by the capillaries originating from a defined TA. Additionally, in each muscle region, the span of individual MVUs that had complete filling was measured as the distance between the collecting venules originating in either direction from the capillaries perfused by a common TA (6).

MVU alignment. The alignment of MVUs along muscle fibers in each study field was characterized as follows: the total distance across muscle fibers encompassed by a pair of MVUs was designated "union" (U); the fraction of this distance common to both MVUs was designated "intersection" (I) (see Fig. 1). The alignment of MVUs along muscle fibers in each study was characterized by measuring the I and U of MVU widths for MVU pairs. In practice, the ratio of I to U provides an index of the alignment between two MVUs; a value of 1.0 indicates that the two MVUs feed the same group of muscle fibers, a value of 0 indicates that the two MVUs have no fibers in common, and values between 0 and 1 indicate that the two MVUs supply some common fibers but also supply fibers that are not common to both MVUs. Within each study field, I/U was determined for adjacent MVU pairs and for MVU pairs separated by one, two, or three MVUs. Adjacent MVUs are referred to as a 1° pair; the latter are referred to as 2°, 3°, and 4° pairs, respectively. The mean distance between the midpoint of neighboring MVUs was calculated from the number of MVUs along the 4-mm reference line.

Model. A computer model was developed to determine the maximum I/U value for randomly placed rectangles. The widths of the rectangles used in the simulation had a normal distribution with the same mean width and SD as we obtained for MVUs sampled in the retractor muscle. For each trial of the simulation, a reference rectangle was selected randomly from the sample and its lower left corner was placed at the origin of a two-dimensional axis. A test rectangle, also selected at random from the population, was then positioned to the right of the reference. The vertical position of the base of the test rectangle was randomly determined, with equal probability of it being placed anywhere within ±1 width of the reference rectangle. Two other test rectangles were then randomly selected and positioned directly above and below the first test rectangle to form a vertical column of three contiguous rectangles adjacent to the reference. The I/U value was calculated for each of the test rectangles relative to the reference, then the largest I/U value of the three was stored. This process was repeated for 8,000 trials, and the mean value was taken as the predicted maximal value of I/U for randomly arranged rectangles.

Statistics. Data were compiled and analyzed with Microsoft Excel (version 5.0, personal computer). Summary data are presented as means ± SE. Comparisons of I/U values among muscle regions (e.g., caudal vs. middle vs. rostral; muscle interior vs. muscle edge) and among MVU pairs (1°, 2°, 3°, and 4°) were performed with analysis of variance. Measured I/U values were compared with values generated by an equivalent number of trials from the computer model by using a t-test. Results were accepted as statistically significant at P <=  0.05.


RESULTS

General features of retractor muscle and its vascular supply. The hamster retractor muscle is of mixed fiber composition (27) and functions to retain the cheek pouch against the body wall (20). The muscles we studied were 30-35 mm in length in vivo; they were ~500 µm thick and ~5 mm wide at the origin and through the midregion, from where they fanned out and became thinner (<= 200 µm) as they inserted onto the cheek pouch over a width of 10-15 mm. The mass of the retractor muscle from similar animals is 80-120 mg (S. S. Segal and D. G. Welsh, unpublished observations). Arteriolar network topology was often tree-like in the thick region, whereas the thin region was characterized by many anastomosing 3A "loops" among 2A branches. Typically, two feed arteries [in vivo diameter ~70 µm (at rest) to ~120 µm (dilated); D. G. Welsh and S. S. Segal] entered the midregion at the medial edge of the ventral surface (see Fig. 1 of Ref. 16) and continued for 200-400 µm as 1A arterioles within the muscle. Each 1A vessel typically gave rise to a pair of interconnected 2A branches that coursed along the muscle axis. Daughter branches typically arose from 2A vessels at right angles (88 ± 2°; n = 156) with an interbranch distance of 0.41 ± 0.02 mm (n = 164) and fell into three categories: 1) TAs (~40%) of individual MVUs; 2) 3A arterioles (~35%) that branched into two or more TAs that supplied corresponding MVUs; and 3) 3A arcade segments (~25%) that formed anastomoses with the same or a different 2A branch and that also gave rise to MVUs.

MVUs in retractor muscles. Figure 1 illustrates the analysis developed for evaluating MVU widths and I/U values. The present I/U data are based on 20 study fields examined in nine muscles. The average distance between neighboring MVUs (0.64 ± 0.01 mm) indicates that ~50 MVUs were required to span the length of retractor muscles. The tracings in Fig. 2 illustrate that MVUs arising from a parent arteriole can range from poorly aligned (Fig. 2A) to well aligned (Fig. 2B) along muscle fibers.


Fig. 2. Line drawings (from video monitor) of MVUs containing Microfil in hamster retractor; muscle fibers (not shown for clarity) are horizontal and parallel to capillaries. These MVUs encompass tissue depth of 2-3 muscle fibers; drawings were made by focusing through muscle. A: three MVUs originating from common parent vessel with minimal overlap between MVUs arising from consecutive TAs along parent arteriole. Note that middle MVU supplies different group of fibers than MVUs on left and right, attributable to different lengths of respective TA branches. With perfusion of entire length of capillaries (as present in vivo), gap between left and right MVU would be eliminated, with respective capillaries supplying same fibers and converging into common collecting venule (3, 6, 14). B: adjacent rows of well-aligned MVUs along muscle fibers, attributable to close proximity of parallel branches of respective parent vessels and nearly uniform lengths of respective TA branches.
[View Larger Version of this Image (36K GIF file)]

The distribution of MVU widths appeared Gaussian (Fig. 3A). On average, the width of MVUs was 0.50 ± 0.01 mm (n = 111), and MVUs perfused segments of ~30 muscle fibers through 2-3 layers (tissue depth, ~100 µm); these features did not differ (P = 0.10) across the caudal, middle, and rostral regions of the retractor muscle. The average muscle fiber length spanned by individual MVUs with complete filling was 0.93 ± 0.07 mm. Thus with MVU dimensions of 0.5 × 0.1 × 1.0 mm (width × depth × length), we estimated that the average volume of muscle supplied by a single MVU was 0.05 mm3, which predicts that each milligram of muscle contains ~20 MVUs.


Fig. 3. A: frequency distribution of MVU widths (n = 111) from all study fields examined for I/U relationships; mean MVU width was 0.50 ± 0.01 mm. B: frequency distribution for all I/U values calculated for study fields within hamster retractor muscles; mean I/U was 0.66 ± 0.02.
[View Larger Version of this Image (18K GIF file)]

The distribution for I/U values was skewed toward the higher end (Fig. 3B), with I/U values in respective muscle regions ranging from 0.06-0.99 (caudal), 0.40-0.91 (middle), and 0.24-0.93 (rostral). The I/U values were not different among regions (P = 0.06), with an overall average of 0.66 ± 0.02. However, values from the interior of muscles were less (P < 0.05) than I/U values determined along the edge of muscles (0.71 ± 0.02), supporting the idea that a physical boundary can influence MVU alignment. Irrespective of muscle region, the alignment of MVUs within study fields did not vary with separation between MVUs (Fig. 4).


Fig. 4. Alignment of MVUs along muscle fibers in 15 study fields located within muscle (to minimize anatomic boundary effect of muscle edges). Values are means ± SE of I/U for 1° (n = 63), 2° (n = 49), 3° (n = 34), and 4° (n = 20) pairs (see Fig. 3B) shown relative to maximum value (dotted line) for randomly aligned MVUs (as described in METHODS). Alignment of MVU pairs was not significantly different across orders (P = 0.7) and was therefore independent of MVU separation.
[View Larger Version of this Image (16K GIF file)]

In approximately one-half of the study fields examined, all MVUs within the field originated from the same parent arteriole (Fig. 2B). In the remaining fields, the TAs that supplied MVUs originated from more than one parent vessel (e.g., Fig. 1B). The alignment of MVUs was not different (P = 0.13) between such networks, which were found, irrespective of muscle region.

Computer model. The model randomly selected rectangles from a normal distribution of rectangles having the same mean width and SD as MVUs in retractor muscles. The assumption of a normal distribution is consistent with the data in Fig. 3A. The model simulated alignment in two dimensions only and assumed that muscle fibers were parallel, as observed in our study fields of retractor muscles. The model also assumed that there were no gaps in tissue perfusion between neighboring MVUs, which is the case in vivo (3, 6). Lastly, the model chose the neighboring MVU with maximum overlap in each trial; this feature was designed to provide an estimate of the maximum value that could be expected for random alignment across a large number of samples. The model predicted that random MVU alignment would result in a maximum I/U value of 0.58, which was less (P < 0.05) than the average value observed throughout the retractor muscle. Because complete alignment of MVUs is indicated when I/U = 1.0 and our measured values were consistently closer to the predicted value, we suggest that the organization of MVUs in the retractor muscle is closer to random than to completely aligned.


DISCUSSION

When a muscle fiber becomes active, its requirements for oxygen delivery and metabolite removal increase along its entire length. However, muscle fibers are much longer than the distance supplied by the capillaries in a single MVU. Therefore, blood flow must increase through many MVUs to perfuse the entire length of a muscle fiber. The accuracy with which blood flow can be controlled to a particular fiber (or to a group of fibers) is determined by how precisely MVUs are aligned along the muscle fiber(s). We have performed the first investigation of this relationship in the parallel-fibered retractor muscle of the hamster. Our analysis used the I/U of neighboring MVU widths as an index of MVU alignment (Fig. 1). Complete alignment is indicated by an I/U of 1.0 (i.e., MVUs within a study field overlay the same group of muscle fibers), whereas random alignment was predicted to result in a maximum ratio of 0.58. In practice, we found that I/U values were 1) closer to the value predicted by the random model; 2) independent of separation between MVUs (Fig. 4); 3) similar across muscle regions with pronounced differences in arteriolar network topology; and 4) greater along muscle edges than within the muscle. Moreover, MVUs within a study field were as often derived from different parent vessels as from the same parent vessel. These findings imply that blood flow cannot selectively increase to a specific muscle fiber or to a particular group of fibers. Rather, blood flow must increase along a relatively wide region of the muscle relative to the locus of muscle fiber activity. Furthermore, vasodilation must encompass multiple parent vessels to increase capillary perfusion along the active muscle fibers.

The average distance between the midpoint of neighboring MVUs was 0.64 mm, whereas the total distance spanned by completely filled MVUs was ~1 mm. This difference implies that there is a degree of overlap among MVUs through fiber layers (i.e., muscle thickness) of the retractor (as found in the hamster tibialis muscle; Ref. 6) that was not accounted for in our two-dimensional analysis of study fields. Nevertheless, our findings indicate that >= 50 MVUs must work together to increase flow to an active fiber. An insightful review (3) has inferred that blood flow to the volume of muscle encompassed by an MVU could be controlled independent of blood flow elsewhere in the muscle. However, because a muscle fiber contracts along its entire length when it is recruited (and will thereby require a corresponding increase in capillary perfusion), it appears unlikely that a vasomotor response would be confined to a single MVU.

The branching of arteriole networks does not consistently follow the organization of muscle fibers, whether fibers are arranged in parallel (e.g., retractor muscle) or have a dispersive organization (e.g., cremaster muscle). Thus the arteriolar network may appear ill-suited to provide blood flow specifically in accord with muscle fiber activity. This impression is highlighted by our finding that 1) the MVUs within a study field were often supplied by different parent arterioles and 2) the proximal and distal regions of the retractor muscle are typically supplied by different feed arteries (16), as seen in other skeletal muscles (30). Moreover, this organization of the resistance network implies that, for capillary perfusion to increase along the length of a muscle, a mechanism is required whereby blood flow into respective MVUs is physiologically coordinated among the parent arterioles. In fact, evidence suggests that cell-to-cell coupling between smooth muscle and endothelial cells enables such coordination of vasomotor activity among arteriole branches (11, 13, 23, 24). Thus in addition to promoting a uniform distribution of pressure and flow within the muscle (8), arteriolar anastomoses could provide a signaling pathway for coordinating MVU perfusion among TAs (22, 23) and respective regions of the muscle. Testing this hypothesis will require additional experiments performed during physiological conditions of blood flow control.

Ascertaining the uniformity of capillary perfusion along muscle fibers will provide a functional correlate to the relationships indicated by the present anatomic data. However, evidence from the cremaster muscle suggests that, even with all capillaries perfused, a heterogeneous distribution of red blood cells within each MVU will place an upper limit on the uniformity of muscle fiber perfusion (5, 7). Nevertheless, any overlap of diffusion fields through the thickness of the muscle could contribute to the homogenous distribution of oxygen among muscle fibers (6). Such an interaction seems particularly apparent in limb muscles (e.g., the hamster tibialis; Ref. 6), which have much greater thickness compared with the retractor (16, 20, 26), cremaster (2, 22, 23), and spinotrapezius (25) muscles more commonly used for microvascular studies. Indeed, the thinness of these latter tissues may constrain the relationship among MVU perfusion fields to more closely approximate a two-dimensional array.

We tested for the possibility that anatomic constraints may promote MVU alignment along muscle fibers by comparing I/U values of MVUs located within the muscle to those located along the edge of the muscle. Indeed, we found significantly greater alignment in the latter case. Separation between groups of muscle fibers could also explain the apparently high degree of MVU alignment in the thin region of the rat spinotrapezius muscle (25). In cases where MVUs were well aligned with parallel parent vessels (Fig. 2B), consecutive TA branches were of uniform length and orientation, which may be enforced by separation between fiber groups. However, consecutive TAs often differed in length, resulting in adjacent MVUs with incomplete overlap (Fig. 2A). Collectively, these findings imply that one determinant of MVU alignment is the variability in the length of respective TAs.

Conclusion. An increase in blood flow to an active muscle fiber without overperfusion of inactive fibers would require MVUs to be no wider than a muscle fiber and completely aligned along the axis of the fiber. However, the present data indicate that neither the size nor the alignment of MVUs is conducive to selectively increasing blood flow to a single muscle fiber, nor even to a particular fiber group. We propose instead that capillary perfusion must increase through relatively broad regions along the muscle to accommodate the metabolic demands of individual muscle fibers.


ACKNOWLEDGEMENTS

We are grateful to Dr. A. J. Fuglevand for assistance with modeling of MVU alignment and for valuable discussion and critique of our work.


FOOTNOTES

   This study was supported by National Heart, Lung, and Blood Institute Grant RO1-HL-56786 and American Heart Association Grant-In-Aid 9300712.

   This work evolved from G. Emerson's Senior Thesis in Chemical Engineering. It was performed during the tenure of an Established Investigatorship Award to S. S. Segal from the American Heart Association and Genentech.

Address for reprint requests: S. S. Segal, The John B. Pierce Laboratory, Yale Univ. School of Medicine, 290 Congress Ave., New Haven, CT 06519 (E-mail: sssegal{at}jbpierce.com).

Received 8 February 1996; accepted in final form 13 August 1996.


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