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Am J Physiol Regul Integr Comp Physiol 280: R156-R165, 2001;
0363-6119/01 $5.00
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Vol. 280, Issue 1, R156-R165, January 2001

Inferences on force transmission from muscle fiber architecture of the canine diaphragm

Aladin M. Boriek, Deshen Zhu, Mark Zeller, and Joseph R. Rodarte

Baylor College of Medicine, Houston, Texas 77030


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Functional properties of the diaphragm are mediated by muscle structure. Modeling of force transmission necessitates a precise knowledge of muscle fiber architecture. Because the diaphragm experiences loads both along and transverse to the long axes of its muscle fibers in vivo, the mechanism of force transmission may be more complex than in other skeletal muscles that are loaded uniaxially along the muscle fibers. Using a combination of fiber microdissections and histological and morphological methods, we determined regional muscle fiber architecture and measured the shape of the cell membrane of single fibers isolated from diaphragm muscles from 11 mongrel dogs. We found that muscle fibers were either spanning fibers (SPF), running uninterrupted between central tendon (CT) and chest wall (CW), or were non-spanning fibers (NSF) that ended within the muscle fascicle. NSF accounted for the majority of fibers in the midcostal, dorsal costal, and lateral crural regions but were only 25-41% of fibers in the sternal region. In the midcostal and dorsal costal regions, only ~1% of the NSF terminated within the fascicle at both ends; the lateral crural region contained no such fibers. We measured fiber length, tapered length, fiber diameters along fiber length, and the taper angle for 271 fibers. The lateral crural region had the longest mean length of SPF, which is equivalent to the mean muscle length, followed by the costal and sternal regions. For the midcostal and crural regions, the percentage of tapered length of NSF was 45.9 ± 5.3 and 40.6 ± 7.5, respectively. The taper angle was ~0.15° for both, and, therefore, the shear component of force was ~380 times greater than the tensile component. When the diaphragm is submaximally activated, as during normal breathing and maximal inspiratory efforts, muscle forces could be transmitted to the cell membrane and to the extracellular intramuscular connective tissue by shear linkage, presumably via structural transmembrane proteins.

micromechanics; functional morphology; respiration; respiratory muscles


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

UNDERSTANDING THE MECHANISM(S) by which force is transmitted in the diaphragm muscle necessitates a precise knowledge of muscle fiber architecture (1-3). In vivo, the diaphragm experiences loads applied both longitudinally and transversely to the muscle fibers, whereas limb muscles primarily experience loading along the long axis of the muscle fibers. Therefore, the mechanism of contractile force transmission in the diaphragm may be more complex than in limb muscles. The mechanical interaction between the cell membrane and the extracellular matrix determines the mechanics of the muscle at the tissue level. The extracellular matrix is mostly collagen. It transmits contractile forces among muscle fibers and through the muscle tendinous junction (MTJ) at either attachment on chest wall (CW) or central tendon (CT). By virtue of the curved surface of the diaphragm, contractile forces are converted to transdiaphragmatic pressure and muscle shortening is converted to volume displacement (6).

Our previous anatomical study (2) demonstrated that 1) there is a small gradient in muscle thickness along the length of muscle fascicles and 2) the inner perimeter of the costal diaphragm, where muscle fibers originate from the CT (origin length), is only 60% of the outer perimeter that inserts on the CW (insertion length). The small thickness gradient was not proportional to the ratio of origin length to insertion length. This discrepancy is incompatible with a muscle consisting only of uniform cylindrical fibers extending from CT to CW. Therefore, we speculated that the diaphragm has discontinuous muscle fiber architecture (2). We also found that fiber density (number) of muscle fibers per cross-sectional area was greatest midway between the CT and CW and that neuromuscular junction (NMJ) bands spanned the muscle surface from CT to CW. Both observations were consistent with a discontinuous fiber architecture in which fibers may not span the entire muscle length between CT and CW.

In this study, we tested the hypotheses that the diaphragm has discontinuous fiber architecture and that fibers terminate within the muscle fascicles by tapering along their length. We determined regional fiber architecture by analyzing fiber lengths, diameters, and cross-sectional areas in the sternal, midcostal, dorsal costal, and lateral crural regions of the left hemidiaphragm. Furthermore, we computed the force distribution between adjacent muscle fibers based on sarcolemmal shape. Our results show that the diaphragm has discontinuous fiber architecture. Most fibers do not span muscle length from CT to CW and most show extended taper. During both normal breathing and maximal inspiratory efforts the diaphragm muscle is submaximally activated (12). Therefore, contractile force would be transmitted in shear via connective tissue and via passive muscle fibers.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Muscle morphology. Eleven mongrel dogs, weighing 15-19 kg each, were killed by intravenous injection of pentobarbital sodium. The left hemidiaphragm, the ribs on which it inserted, and portions of the central tendon were removed together and placed immediately in a physiological saline solution. In all 11 dogs, we excised portions of the midcostal region and the lateral crural region. In five dogs, we excised the sternal region of the diaphragm, where muscle length is smallest. In three dogs, we also dissected portions of the dorsal costal region, where the muscle is relatively thin compared with other regions of the costal diaphragm (2, 18). The excised portions of the diaphragms were cut along the muscle fascicles from CT to CW (see Fig. 1). A muscle fascicle is a bundle of fibers, easily identified by the naked eye, that is separated by connective tissue and appears to run the entire length of the muscle from origin on CT to insertion on CW.


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Fig. 1.   Schematic of dog diaphragm viewed from abdominal surface showing locations of different regions from which single muscle fibers were dissected. These regions are sternal, midcostal, dorsal costal, and lateral crural from the left hemidiaphragm. Those are the same regions where measurements of thickness and length were made in a previous anatomic study of the dog diaphragm (2).

To obtain single muscle fibers for quantitative analysis, we removed ~50 fascicles from the sternal region, 260 from the midcostal, 225 from the lateral crural, and 100 from the dorsal costal. Each fascicle contained between 20 and 30 muscle fibers. These fascicles were stained with gold chloride (22) by being fixed in a 25% solution of formic acid for 1-2 h, blotted, and immersed in a 1% solution of gold chloride. After 6-12 h immersion, the fascicles were washed for 12 h in running tap water. To remove connective tissue, the fascicles were incubated in 10% nitric acid solution on an agitation bench (RotoMix type 48200) for 2-3 days. When single fibers began to separate from the fascicles, the acid was diluted with a large volume of water at room temperature. Fascicles were then taken through a graded series of glycerin solutions (50, 70, 80, and 100%, for 2-3 days each) and transferred to 100% glycerin-filled petri dishes. Single fibers then were stripped away from the fascicle with very fine forceps and needles.

The fractions of spanning fibers (SPF), which ran uninterrupted from one insertion site to the other, and non-spanning fibers (NSF), which ended intrafascicularly by tapering, were recorded. We analyzed all fibers within a fascicle, except for broken fibers (5-10% of the total). In fascicles from three diaphragms, we noted the longitudinal position of single muscle fibers within the fascicle and recorded the number of NSF that attached to either CT, CW, or neither. To estimate the number of NSF that inserted on a region of the CW, we multiplied the sampled number of NSF that inserted on a finite length of CW by the ratio of CW insertion length to CT origin length and then divided this figure by the total number of fibers sampled to determine the fraction of NSF that inserted on CW. The fraction of NSF that inserted on CW in the dorsal costal and lateral crural regions was calculated in the same way.

The isolated fibers were examined with a dissecting microscope (Zeiss Axioplan) fitted with a camera lucida attachment. Fibers were mounted on glass slides in glycerin jelly, and morphological characteristics were measured at a magnification of ×20 using light microscopy and the BioQuant System IV software (R & M Biometrics, MEGm, vol. 305, version 2.10.92). Morphological measurements of muscle fibers included length and repetitive measurements of diameters along the fiber length. The tapered region was defined as the region between the tip of the fiber and the point where the diameter reached 90% of its maximum as previously described by Callister et al. (8). The taper angle is the angle at which the surface of a single fiber intersects the longitudinal axis of the fiber. This angle was estimated by using the BioQuant System to measure fiber diameter at several points along the tapered regions and the longitudinal distances between the points of measurements. The slope of the fitted line of those points on the surface of the tapered region is the tangent of the taper angle.

Muscle shrinkage. We measured the relaxed length of freshly excised diaphragm strips and the length of SPF isolated from the same region after fixation. The difference between these values was used to assess muscle shrinkage for each region examined. Shrinkage due to histochemical processing was found to be ~33, 31, and 22% in the costal, crural, and sternal regions, respectively.

Sarcomere length measurements. We measured sarcomere lengths in the diaphragms of three mongrel dogs (15-20 kg; dogs 9, 10, and 11 in Tables 1 and 2). Fibers sampled from the midcostal, dorsal costal, and crural regions were fixed at resting length, which approximates muscle length at functional residual capacity. These fibers included SPF, NSF that originated on CT or inserted on CW, and NSF that reached neither CW nor CT. Images of individual fibers were captured using the Sony CCD-IRIS colored camera and the software program Snappy video snapshot, calibrated using a 0-1 mm/100 objective micrometer, and the images were stored on an XPS R350 personal computer. Sarcomere length was calculated as the average of 10 adjacent sarcomeres. Three areas on each fiber were measured in this way using the Image Tool Program ver. 2.0 at ×1,000.

                              
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Table 1.   Occurrences of spanning and non-spanning fibers


                              
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Table 2.   Occurrences of NSF inserting from CT or CW

Statistical analyses. We fit the sarcomere data to a linear regression model that accounted for the following parameters: region (midcostal, dorsal costal, lateral crural, and sternal), insertion (CT, CW, neither, or both), and taper (tapered or nontapered). Dog was a blocking variable, and pairwise interactions between region, insertion, and tapering were also included in the model.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Diaphragm fibers fell into four categories: 1) SPF that ran between the origin on CT and insertion on CW (Figs. 2C and 3C), 2) NSF that inserted on CW (Fig. 3B), 3) NSF that originated on CT (Fig. 2B), and 4) NSF tapered at both ends that did not originate on CT or insert on CW (Figs. 2A and 3A). NSF typically had a consistent diameter that tapered at one end to a fine threadlike termination. The nontapered ends of NSF fibers attached to CT or CW appeared rounded; we could not detect any tendinous attachments at the tapered ends. In comparison, SPF appeared to have a relatively consistent diameters along its length.


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Fig. 2.   Comparisons of different fiber types from the costal region of the same dog diaphragm muscle. A: a single non-spanning fiber (NSF) that inserts on neither the chest wall (CW) nor central tendon (CT). A1: the entire muscle fiber at ×2.5. A2 and A3: tapered ends of the fiber at ×250. Striations are visible throughout the tapering region of the fiber. B: a single NSF that inserts on the CT. B1: the entire muscle fiber at ×2.0. B2: intramuscular tapered end of the fiber at ×250. The tapered ends of the fiber are morphologically similar to their nontapering regions, and striations are visible throughout tapering region. No special attachments or other structures related specifically to the tapered free ends could be resolved by light microscopy. B3: the rounded ends characteristic of blunt-type endings of the fiber at ×250. C: a single spanning muscle fiber. C1: the entire muscle fiber at ×1.9. C2 and C3: the rounded ends characteristic of blunt-type endings of the fiber at ×250.



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Fig. 3.   Comparisons of different fiber types from the crural region of the same dog diaphragm muscle. A: a single NSF that inserts on neither CW nor CT. A1: the entire muscle fiber at ×3.0. A2 and A3: tapered ends of the fiber at ×250. Striations are visible throughout the tapering region of the fiber. B: a single NSF that inserts on CW. B1: the entire muscle fiber at ×2.0. B2: intramuscular tapered end of the fiber at ×250. B3: a rounded end characteristic of blunt-type ending of the fiber at ×250. C: a single spanning fiber. C1: the entire muscle fiber at actual size. C2 and C3: a rounded end characteristic of blunt-type ending of the fiber at ×250.

Occurrences of SPF and NSF in the sternal, midcostal, and lateral crural regions of diaphragms from 11 mongrel dogs are shown in Table 1. Most NSF were attached to either CT or CW and terminate intrafascicularly by tapering to very fine strands. In the sternal region, the majority of single muscle fibers was SPF, and no fibers were found that terminated intrafascicularly at both ends. In contrast, the majority of muscle fibers in midcostal, dorsal costal, and lateral crural regions was NSF. The percentage of NSF was significantly smaller in sternal region than any of the other regions (P < 0.0001).

The nature of NSF attachments of single muscle fibers from different diaphragm regions is shown in Table 2. In the midcostal diaphragm, the percentage of NSF that inserted on CT is not significantly different from the percentage of those that inserted on CW (P = 0.25). In the dorsal costal and crural regions, more NSF inserted on CW than CT (P = 0.004). Only ~0.5% of all fibers tapered at both ends.

The ratio of SPF and NSF that insert on CW or CT, corrected for the different insertion lengths of CT and CW, is shown schematically for the midcostal, dorsal costal, and lateral crural regions in Fig. 4. The ratio of fibers that insert on CT to fibers that insert on CW in the midcostal and dorsal costal regions is ~0.6:1.0, with the ratio slightly higher in the midcostal; this ratio is ~1.2:1.0 in the lateral crural region. Figure 4 also shows the overlap of NSF midway between CT and CW in each of the three regions.


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Fig. 4.   Schematic representation of the actual proportion of muscle fibers inserting on CT or CW and spanning (SPF) from CW to CT in the crural, midcostal, and dorsal costal regions of the left hemidiaphragm. NSF taper to a very fine thread within the muscle. Fibers that tapered at both ends comprised less, ~1% of each region, and are not shown. Lengths of NSF and SPF within each region are approximately proportional to the actual fiber lengths. Lengths of insertion on CW and CT in the costal and crural regions are approximately proportional to the actual insertion of insertion, P, of the diaphragm. In the costal region, P(CT):P(CW) is 0.6:1.0, and in the crural region, P(CT):P(CW) is 1.2:1.0 (2). The proportion of each type of fiber within a region was determined using three values: 1) the total number of NSF inserting on the longer insertion multiplied by the ratio of longer insertion to smaller insertion, 2) the total number of NSF inserting on the smaller insertion, and 3) the total number of SPF (Table 2).

The percentage of occurrence of NSF of lengths between 1 and 5 cm in the midcostal and lateral crural regions of the diaphragm is shown in Fig. 5. There were no fibers inserting on CT in the midcostal diaphragm that were longer than 4 cm. Furthermore, very few crural muscle fibers were shorter than 2 cm. The percentage of fibers that were 2-3 cm long was significantly greater in the midcostal than in the lateral crural region (P < 0.01). In contrast, the percentage of muscle fibers that were 3-4 cm long was greater in the crural than in the midcostal region of the diaphragm (P < 0.01). In the midcostal and lateral crural regions of the diaphragm, the length of muscle fibers inserting on CW was not statistically different from the length of the fibers inserting on CT (P = 0.095 and P = 0.12, respectively). The muscle length of fibers inserting on CT was longer in the crural region than in the midcostal diaphragm (P < 0.001). Furthermore, muscle fibers that insert on CW are longer in the lateral crural than in the midcostal region (P < 0.001).


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Fig. 5.   Percentage of occurrence in costal and crural region of the diaphragm of NSF inserting on CT and on CW that are 1-5 cm long. No fibers longer than 4 cm inserted on CT in the costal (Cos) muscle, and very few crural (Crur) muscle fibers were shorter than 2 cm.

Fiber lengths are listed in Table 3. Differences in the amount of shrinkage of SPF after histochemical treatment were negligible across regions, except between the sternal and midcostal regions and between the midcostal and dorsal costal regions (P < 0.0005 for both). Length of SPF was greatest in the crural region, whereas the length of SPF and NSF was smallest in the sternal region. Length of the overlapping region among adjacent muscle fibers, estimated from the mean length of NSF inserting on CW or on CT and of mean length of SPF, was 0.5 ± 0.1 cm in the costal diaphragm and 1.6 ± 0.2 cm in the crural diaphragm. Mean taper angle of the fiber end was 0.15 ± 0.06° for fibers that tapered at one end and 0.15 ± 0.02° for fibers that tapered at both ends. Taper regions from representative fibers of the crural and costal regions are shown in Fig. 6.

                              
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Table 3.   Fiber length and tapering characteristics



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Fig. 6.   Plot of the radius of the tapering end along the length of the tapering region of typical NSF from the lateral crural and midcostal regions. The taper angle was calculated as the arctan of the slope of the fitted line to the tapering region, determined as the region from the end of the fiber to the first point where the diameter reached 90% of its maximum. The tapering angle was 0.15 ± 0.03° in the crural and 0.15 ± 0.02° in the midcostal.

Examples of fiber architecture complexity are shown in Fig. 7. One arrangement (Fig. 7A) is composed of three NSF from the costal region (Tcw1, Tcw2, and Tcw3) inserting on CW and adjacent to the surface of an NSF that is tapered and inserting on CT (Tct). A second architectural arrangement (Fig. 7B) is composed of a bundle inserting on CT and two NSF from the midcostal region (Tct1 and Tct2), which are adjacent to the surface of an NSF that is tapered and inserting on CW (Tcw). The tapered end of the fiber Tcw is applied to the surface of an SPF. A third architectural arrangement (Fig. 7C) is composed of a bundle of four tapered NSF from the midcostal region (Tct1, Tct2, Tct3, and Tct4). These fibers insert on CT and taper into very fine strands within the muscle fascicles.


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Fig. 7.   A: 3 NSF from the costal muscle of the diaphragm that insert on the CW (Tcw1, Tcw2, and Tcw3) applied to the surface of an NSF that is tapered and inserts on the central tendon (Tct). B: a bundle of 2 midcostal NSF (Tct1 and Tct2) that insert on CT, applied to the surface of an NSF that is tapered (Tcw) and inserts on CW. The tapered region of Tcw is applied to the surface of an SPF. C: a bundle of 4 tapered NSF from the costal region of the diaphragm (Tct1, Tct2, Tct3, and Tct4). These fibers insert on CT and taper into very fine strands; magnification, ×8.8.

There were no significant differences in the average sarcomere length among different regions: midcostal, dorsal costal, and lateral crural regions. However, sarcomere length differed between tapering and nontapering regions of fibers (Fig. 8A) and among different sites of insertion within each region (Fig. 8B). There was also a significant difference in sarcomere lengths in tapering and nontapering regions depending on the site of insertion (P = 0.003). The largest mean sarcomere length in fibers tapered at both ends was found in dorsal costal fibers; however, dorsal costal fibers that inserted on CW or CT had smaller mean sarcomere lengths than fibers with the same insertion sites from other diaphragm regions.


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Fig. 8.   A: comparison of normalized mean sarcomere lengths between tapering and nontapering regions of fibers. Mean sarcomere lengths differed significantly between the tapering and nontapering regions of fibers (P < 0.001). The normalized length of 1 is equal to 1.76 µm. B: comparison of normalized sarcomere lengths within the dorsal costal, lateral crural, and midcostal regions of the diaphragm depending on the site of insertion of the muscle fiber (CW; CT; S, both; or BT, neither). The mean length of sarcomeres from a specific region and site of insertion differed significantly from that of sarcomeres from other regions and sites of insertion (P < 0.001). The greatest mean sarcomere length in BT fibers was found in fibers from dorsal costal region; however, mean sarcomere lengths in CT and CW fibers from dorsal costal were smaller than mean lengths of CT and CW fibers from the other regions. The normalized length of 1 is equal to 1.80 µm.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Our results show that the diaphragm muscle has a discontinuous fiber architecture in which short muscle fibers terminate by gradually decreasing their cross-sectional area along their length. In this architecture, contractile forces are transmitted from one tapering fiber to its neighbor mostly in shear presumably via membrane-associated structural proteins. Therefore, the mechanism by which forces are transmitted among muscle fibers in a discontinuous architecture is more complex than in a continuous muscle fiber architecture. In a muscle fascicle composed of fibers that attach at each end to an extracellular matrix through an MTJ, forces are tensile and are transmitted in the direction of the muscle fiber from the MTJ at CT to another at CW. However, a discontinuous fiber architecture cannot exert purely tensile forces against a conventional tendon. Instead, force must be distributed among neighboring fibers through the extracellular matrix (11).

It has been suggested that the force of hindlimb muscle contraction is transmitted from muscle fibers to the endomysial connective tissue (24). Street's study (21) on frog semitendinosus (ST) muscle showed that both active and passive forces were transmitted to the connective tissue, presumably the endomysial layer that envelopes the muscle fiber. If myofibrils within the cell were linked at various points along the sarcolemma, then those portions of the cell could apply force by pulling against one another (20). The diaphragm of either the rat or the rabbit has a single motor endplate band across its muscle (10). On the basis of the assumption that most skeletal muscle fibers are singly innervated, the diaphragms of either the rat or rabbit are primarily composed of fibers that span the entire muscle length. The muscular portion of the diaphragm in these species is longer than the ST muscle of the frog. Therefore, frog ST may also be composed of fibers that span its entire length. To the extent this is true, Street's observations suggest that 1) forces can be transmitted among spanning muscle fibers through connective tissue and 2) the mechanism of force transmission is shear.

It is interesting that in many other muscle types across species where loading is different from the diaphragm, muscle fibers commonly end intrafascicularly and many of these fibers taper at their unattached end. For example, the hindlimb muscles of the cat have discontinuous fiber architecture (17); however, within the same species, the muscles of the hindlimb are longer than the diaphragm muscle. Therefore, in addition to loading, muscle length appears to be a critical determinant of fiber architecture. On the basis of the assumption that most muscle fibers are singly innervated, the central region near the NMJ in a long muscle fiber would relax before an electric signal could propagate to the ends of the fiber (17).

Mean length of muscle fibers in all regions of the canine diaphragm is <5 cm, which theoretically should not impede synchronous contractions of the sarcomere units within a muscle fiber. Therefore, muscle length is not the only determinant of muscle fiber architecture. The diaphragm is a membrane that is loaded with pressure in vivo (4, 19). Muscle force is only generated along the fibers. Furthermore, the diaphragm is submaximally activated during both quiet breathing and maximal inspiratory efforts (12). Therefore, in a muscle with discontinuous fiber architecture, it would be important for force to be transmitted between active muscle fibers and passive fibers.

In discontinuous fiber architecture, if all muscle contractile forces were transmitted via the sarcomeres arranged in series, the sarcomeres in the tapered region of a fiber would have to tolerate the same tensile force exerted by sarcomeres in nontapered regions (8). Thus muscle stress would be much greater in tapered regions than nontapered regions. To permit an alternative force transmission vector, forces may instead be transmitted tangentially along the length of a fiber to the extracellular matrix and cell membrane. Primary candidates for force transmission along the cell membrane are membrane-associated structural proteins (e.g., the integrins and associated structural proteins and the dystrophin complex) (23). These proteins are concentrated at muscle fiber ends where active and passive forces would be transmitted axially across the cell membrane. However, these proteins are also enriched in periodic structures, called costameres, at the surface of muscle fibers. The localization of costameres suggests that they function in the transmission of muscle forces applied in the transverse plane of the cell. Transmembrane molecules that associate intracellularly and extracellularly with tensile structures such as thin filaments and collagen fibers may indeed undergo tensile loading. However, as they are loaded, these forces are primarily in the plane of the membrane, not perpendicular to it. Thus, if we regard the membrane as a composite structure containing elements that experience tensile, compressive, and shear loading, the net stress seen by the interface is essentially shear.

Callister et al. (8) discussed the functional effect of muscle fiber tapering on the rate of membrane current spread into the tapered ends. One possibility is that muscle fiber tapering will slow action potential propagation because sarcolemmal conduction velocity is proportional to muscle fiber diameter, which would degrade the response speed of muscle cells that taper over a large fraction of their length. However, if the tapered ends contain a lower density of t-tubular material, this would decrease the fiber's capacitance and increase conduction velocity (8).

The architectural complexities of motor units influence the mechanical interactions among muscle fibers. The forces applied to an individual fiber are affected by the activation and spatial arrangement of neighboring motor units (16). During most contractions the diaphragm is submaximally activated. That is, only a fraction of muscle fibers are contracting. Forces will be transmitted in shear among adjacent active and passive muscle fibers. Muscle force is affected by the degree of motor unit recruitment and by the compliance of passive fibers. The presence of many passive muscle fibers could damp the transmission of muscle force developed by an active muscle fiber (24). During passive deflation, however, the diaphragm is subjected to pressure and the entire diaphragm membrane is loaded with tension. The membrane of the diaphragm is anisotropic, and membrane passive principal tensions are essentially oriented in the directions of muscle fibers and transverse to the muscle fibers (4, 19).

Our results show that all fibers shorter than the length of the muscle are tapered. In tapered fibers, contractile forces could be transmitted to the endomysium through the sarcolemma along the length of the tapered region (8, 11, 24-26). Shape and length of the tapered portions of the fiber are important mechanical parameters that determine stress distribution at the interface between the endomysial connective tissue and the muscle fiber. For example, the surface area is amplified at the end of an NSF relative to the cross-sectional area. Figures 2 and 3 contrast the shapes of tapered ends of fibers to those of nontapered ends in the crural and costal regions. In the tapered region of a muscle fiber, the taper angle determines the mechanism of force transmission between muscle fiber and extracellular matrix. Stress generated by a tapered muscle fiber, sigma fiber, can be transmitted in the tapered region by two components: 1) tensile stress perpendicular to the surface of the fiber membrane, Tper = sigma fibersin2Theta , where Theta  is the angle of taper at the end of a muscle fiber and 2) shear stress parallel to the surface of the fiber, tau par sigma fibersinTheta cosTheta , (14, 15). A very small taper angle creates an interface between muscle fiber and extracellular matrix that is essentially loaded in shear (Fig. 9). For taper angles close to 0.15°, as we observed in NSF (Table 3 and Fig. 6), the shear component of tension is (2.62×10-3 ± 3.49×10-4)sigma fiber, ~380 times greater than the tensile component, (6.85×10-6 ± 1.22×10-7)sigma fiber. Furthermore, a very small taper angle ensures that shear stress is essentially constant along the tapered portion of the muscle fiber, minimizing stress concentration at the end of the fiber (9, 24). On the contrary, if NSF had blunt ends, shear stress would be nonuniform and concentrated at the ends of the fibers. This would increase the likelihood of mechanical failure at the fiber ends. An extensive folded interface exists between the diaphragm muscle fiber and tendon. Forces transmitted between the tendon and the fiber are distributed over a large area of the folded interface. Therefore, muscle stress at the MTJ should be small (23).


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Fig. 9.   Diagram showing stress distribution generated by an NSF along its tapering region. As fiber A contracts, it transmits a total force of sigma fiber through its membrane to fiber B in the direction longitudinal to the axes of the fibers. The angle of taper, Theta , is measured from the longitudinal axis of a fiber to its surface. As this angle increases, a greater proportion of force is transmitted in the tensile direction, T, than in shear, tau . Our taper angle measurements of 0.15° indicate that the shear component is ~380 times greater than the tensile component.

The distribution of muscle fibers of the diaphragm shown in Fig. 4 demonstrates that NSF overlap near the center of each region. It is possible that NSF transmit forces to CT or CW via costameres to adjacent fibers or via passive elements such as the cell membrane and the extracellular intramuscular connective tissue. Those NSF are adjacent to other fibers that connect directly to CT or the CW. Uniform shortening of sarcomeres in these two classes of fibers would require slippage. However, possibly the linkages of collagen fibers with adjacent muscle fibers may prevent slippage. An alternative and perhaps more reasonable model would be if forces in one NSF were transmitted to another adjacent muscle fiber so that, in essence, those adjacent fibers are in series. Slippage is not needed in such a scenario where muscle fibers are mechanically connected in series.

Many different arrangements among fibers are possible (Fig. 7). NSF from either insertion or origin are not necessarily connected in a 1:1 relationship. In the midcostal region, the percentage of NSF that originates from CT is statistically the same as the percentage that inserts on CW (P = 0.25) (Table 2). However, the length of origin of costal muscle at CT is ~60% of the length of the insertion on CW. When the ratio of fibers that insert on CT to fibers that insert on CW is corrected for the different insertion lengths of CT and CW, the corrected ratio is ~0.6:1.0 (2), approximately the same ratio as the length of CT insertion to the CW insertion. In the crural diaphragm, ~44% more NSF insert on CT than on CW when fibers are counted over the same insertion length of CT and CW. The corrected ratio of fibers inserting on CT to fibers inserting on CW is ~1.2:1.0, the same as the ratio of CT insertion length to CW insertion length. Fibers therefore appear to be uniformly distributed along CT and CW in both the costal and crural regions. In the costal region, this distribution is consistent with the essentially constant thickness of the muscle between CT and CW (2). However, thickness of the crural muscle is ~25% less near CT than near CW. This difference in muscle thickness may be due to a greater proportion of connective tissue near CW.

Our previous physiological in vivo data in the dog (6) demonstrated that during spontaneous breathing, strain perpendicular to the long axis of the fibers is negligible and muscle shortening is nonuniform in the costal region. In this study, the diaphragm shortened by ~30% more in the central region of the muscle than it did near CT or CW. Because muscle is essentially incompressible, local shortening should be proportional to thickening. The region midway between CW and CT has 1) the greatest fraction of fibers per cross-sectional area due to the tapering and overlap of NSF (Fig. 4) and 2) the smallest proportion of connective tissue to muscle fibers (1). Because connective tissue is at least two orders of magnitude stiffer than active muscle fibers, this region of the diaphragm should have greater passive compliance than regions near insertion on CT or CW. It is possible that regional differences in the proportion of connective tissue to muscle fibers are partly responsible for the observed nonuniform muscle shortening along the length of the bundle. Alternatively, there could be preferential recruitment for those short muscle fibers that are located in the middle of the muscle and do not reach either insertion on CT or CW.

Our investigation of NMJ of the canine diaphragm demonstrated that the number of NMJ was directly proportional to the length of the muscle (1). This is consistent with results from the current study, which demonstrated that the smallest proportion of NSF was found in the sternal region of the diaphragm where muscle length is shortest (Table 3). However, despite the fact that the crural muscle is longer than the costal muscle, there was no significant difference between the proportion of NSF in the costal and crural regions (Table 1). The proportion of SPF within the costal and crural regions was also similar, and therefore the proportion of connective tissue, the remaining major component, is also similar in these two regions. It is possible, however, that the connective tissue in the crural diaphragm may be less uniformly distributed than in the costal diaphragm. As stated earlier, near CW, proportion of connective tissue in the crural may be larger than in the costal muscle.

SPF and NSF do not appear to exhibit different contractile properties. Previous studies (5) demonstrated that the dog midcostal diaphragm consists mainly of two types of motor units, type I slow-twitch fibers and type IIa fast-twitch fatigue-resistant fibers. There are very few type IIx fast-twitch fatigue intermediate fibers and no type IIb fast-twitch fatigable fibers. We determined fiber type in three different transverse sections along the length of the muscle, and found no regional differences in fiber types along the length of the muscle. Because the distribution of ratio of numbers of NSF to numbers of SPF differ significantly along the length of the midcostal diaphragm muscle, we conclude that the fiber type of NSF is not significantly different from those of SPF.

The length of sarcomeres did not vary significantly among fibers with different sites of insertion or among fibers from different regions. However, sarcomere lengths did differ significantly among sarcomeres from tapering and nontapering regions of fibers, with a greater mean length in nontapering fibers (Fig. 8A). Sarcomere length may therefore be a function of the fiber diameter. Hijikata et al. (13) found that sarcomeres were shorter in tapering regions of fibers and that these shorter sarcomeres expressed more tension than longer, more centrally located sarcomeres. Burton et al. (7) measured sarcomere length during isometric contraction and found that sarcomeres at the end shortened while sarcomeres in the center elongated. Therefore fibers should shorten the most midway between CT and CW, and this is in agreement with our previous data (6).

Because we passively stretched the fibers to a length that is equivalent to resting length before measuring the sarcomeres, this stretch may have increased the differences in the sarcomere lengths that were recorded. The mean length of sarcomeres from a specific region and site of insertion also differed significantly from that of sarcomeres from other regions and sites of insertion (Fig. 8B). If the histochemical treatment caused the diaphragm to shrink nonuniformly, sarcomeres in spanning fibers, whose ends are fixed at CT or CW, would be expected to shrink the least and fibers tapered at both ends, which have no fixed ends, would be expected to shrink the most. This is true in the lateral crural region, but the midcostal and dorsal costal regions deviate from this pattern (Fig. 8B). These deviations may be due to the small sample size of fibers tapered at both ends in the dorsal costal region. Alternatively, sarcomeres may shrink uniformly and differences in sarcomere length after histochemical treatment may, therefore, reflect actual differences before treatment.

Perspectives

In this study we investigated fiber architecture of the diaphragm muscle, and we showed the architecture to be complex and mostly discontinuous. That is, there are fibers that either span the entire length of the muscle or terminate by tapering before reaching either or both attachments. In general, NSF are tapered fibers, and, therefore, contractile forces are likely to be transmitted from the tapered fibers along the cell membrane to other adjacent muscle fibers by shear linkage, presumably via structural transmembrane proteins. The tapered length and shape of the NSF could therefore affect the distribution of forces transmitted through the interface between the cell membrane and the extracellular matrix. The diaphragm muscle is submaximally activated during normal breathing and maximal inspiratory efforts and, therefore, the discontinuous fiber architecture with mostly short tapering muscle fibers should allow contractile muscle force to be transmitted from the active fibers to the adjacent passive fibers via shear. Transmembrane structural proteins could transmit muscle force between the cytoskeleton and the extracellular matrix. Therefore, investigating the mechanical role of such proteins should improve our understanding of the mechanism(s) of force transmission in skeletal muscles.


    ACKNOWLEDGEMENTS

The authors thank Ann Marie Doneski, Muffasir Badshah, and Chad Abraham Shaw for technical assistance.


    FOOTNOTES

National Heart, Lung, and Blood Institute Grants HL-54198 and HL-46230 supported this work.

Address for reprint requests and other correspondence: A. M. Boriek, Pulmonary Section, Suite 520B, Dept. of Medicine, Baylor College of Medicine, One Baylor Plaza, Houston, TX 77030 (E-mail address: boriek{at}bcm.tmc.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 6 October 1999; accepted in final form 22 August 2000.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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Am J Physiol Regul Integr Comp Physiol 280(1):R156-R165
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