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Passive mechanics of muscle tendinous junction of canine diaphragm

Department of Medicine, Baylor College of Medicine, Houston, Texas

Submitted 30 July 2004 ; accepted in final form 18 November 2004

	ABSTRACT

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The diaphragmatic muscle tendon is a biaxially loaded junction in vivo. Stress-strain relations along and transverse to the fiber directions are important in understanding its mechanical properties. We hypothesized that 1) the central tendon possesses greater passive stiffness than adjacent muscle, 2) the diaphragm muscle is anisotropic, whereas the central tendon near the junction is essentially isotropic, and 3) a gradient in passive stiffness exists as one approaches the muscle-tendinous junction (MTJ). To investigate these hypotheses, we conducted uniaxial and biaxial mechanical loading on samples of the MTJ excised from the midcostal region of dog diaphragm. We measured passive length-tension relationships of the muscle, tendon, and MTJ in the direction along the muscle fibers as well as transverse to the fibers. The MTJ was slack in the unloaded state, resulting in a J-shaped passive tension-strain curve. Generally, muscle strain was greater than that of MTJ, which was greater than tendon strain. In the muscular region, stiffness in the direction transverse to the fibers is much greater than that along the fibers. The central tendon is essentially inextensible in the direction transverse to the fibers as well as along the fibers. Our data demonstrate the existence of more pronounced anisotropy in the muscle than in the tendon near the junction. Furthermore, a gradient in muscle stiffness exists as one approaches the MTJ, consistent with the hypothesis of continuous passive stiffness across the MTJ.

respiratory muscles; mechanics; stress; strain

Our previous study of in vivo mechanics of canine diaphragm showed substantially smaller mechanical strain in the TF compared with AF direction (8). Furthermore, our in vitro mechanics studies of the diaphragm have demonstrated that the muscle of the diaphragm is anisotropic with less muscle compliance in TF than AF (1, 2, 6). Our finite-element membrane model of the passive diaphragm demonstrated that an inextensible cap simulating the central tendon and anisotropic skirt simulating the muscular portion of the diaphragm would change curvature less than a uniform homogeneous isotropic elastic material would when inflated (5). This study suggested but did not prove that both the central tendon inextensibility and muscle anisotropy contribute to restricting changes of diaphragm shape observed in vivo during physiological loading (3, 7).

In this study, we investigated the mechanics of the MTJ of the canine diaphragm in vitro during uniaxial and biaxial mechanical loading conditions. We hypothesized that 1) the central tendon possesses greater passive stiffness than adjacent diaphragmatic muscle, 2) the diaphragm muscle is anisotropic, whereas the central tendon near the MTJ is essentially isotropic, and 3) a gradient in passive stiffness exists as one approaches the MTJ. To test these hypotheses, we measured uniaxial and biaxial passive length-tension relationships of canine diaphragmatic muscle-tendon strips AF and TF. We found that the MTJ sheet is more compliant and considerably more extensible AF than TF. Furthermore, the central tendon was considerably stiffer than adjacent muscle. In addition, the central tendon near the MTJ was essentially isotropic, whereas the adjacent muscle was anisotropic. We also found that passive stiffness increased gradually as one approaches the MTJ.

	METHODS

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Diaphragmatic muscle strip preparation.   Dogs were maintained according to the National Institutes of Health Guide for the Care and Use of Laboratory Animals, and procedures were approved in advance by the Institutional Review Board of Baylor College of Medicine. Fourteen mongrel dogs (22.4 ± 5.7 kg) were anesthetized with intraveneous injections of pentobarbital sodium (30 mg/kg body wt). The left hemidiaphragm was excised from each animal and immediately immersed in a muscle bath containing modified Krebs-Ringer solution (in mM: 137 NaCl, 5 KCl, 1 NaH₂PO₄, 24 NaHCO₃, 2 CaCl₂·2H₂O, 1 MgSO₄·7H₂O, pH 7.4) bubbled with 95% O₂-5% CO₂ and maintained at room temperature throughout the preparation and experimental phases of this study (10). Animals were euthanized using an overdose of pentobarbital. A 5 x 5 cm portion of muscle tendon was carefully dissected near the midcostal region of the left hemidiaphragm. A muscle-tendon strip was cut along the predominant direction of muscle fiber orientation to minimize damage to the tissue. Overhand knotted black sutures (size 3-0 round-tip surgical needle) were sewn on the thoracic diaphragmatic surface with surgical knot on the opposing abdominal surface to secure each marker in place. These position makers quantified tissue displacement during tissue elongation. To test our first and second hypotheses, we placed eight position markers in a rectangular configuration (1 cm apart) perpendicular to the axis of the MTJ. To test our third hypothesis, we used a second protocol, whereas the number of position markers was increased to 12. In these configurations depicted in Fig. 1, two rows of markers were aligned AF and multiple pairs were aligned TF, thereby allowing assessment of displacements AF as well as TF. Importantly, all markers were positioned in the central region of the tissue to minimize the edge effects of applied load as described by the St. Venant's Principle of Mechanics (11).

View larger version (25K): [in this window] [in a new window]   Fig. 1. Configuration of the position markers placed on the tendon, on the muscle-tendinous junction (MTJ), and on the muscle. Four markers were placed at the tendon near the MTJ (region 1), and those markers were used to compute mechanical strain in the tendon. The 4 markers indicated by region 2 were used to compute strain in the MTJ domain. Markers placed on the muscle near the MTJ were used to compute mechanical strain in the muscle (first experimental protocol: region 3; second experimental protocol: regions 3–5). For the experimental protocol used to simultaneously test hypothesis A and hypothesis B, we utilized the 8-marker configuration (regions 1–3; uniaxial data in Fig. 2 and biaxial data in Fig. 3). For the experimental protocol specifically used to test hypothesis C we utilized all 12-marker configurations (regions 1–5; uniaxial data in Fig. 4).

Computation of two-dimensional strains.   The strains in the plane of the muscle, MTJ, and central tendon were computed by the following procedure. The marked region is divided into triangles with markers forming the apices. Subsequently, the four sutured markers would define four triangles. For example, triangle A is defined by markers 1–3, whereas triangle B would be defined by markers 1, 2, and 4. The coordinates of these points in that unstressed plane of the diaphragm are denoted x_i and y_i (i = 1, 2). The displacement, u_i, from the unstressed state to the deformed state is assumed to be a linear function of position and computed as follows:

This equation with known values of the displacements and the position of three markers substituted for u_i, x_i, and y_i provided a set of three equations for the three coefficients: a₁, a₂, and a₃. Similarly, the data provided the information required for determining the coefficients (a₄, a₅, and a₆) in the following equation:

The values of the coefficients a₁, a₂, etc. were used to find the partial derivatives, which were substituted into the following equations:

where u and v denote the marker's displacement in the x (AF) and y (TF) directions, defined to calculate strains. The strains _x and _y were computed for each triangle. _x is strain in the AF direction, whereas _y is strain in the TF direction, and _xy is shear strain.

where is the extension ratio or the ratio of muscle length at a stretched state relative to the unstressed length. The is mechanical strain either in AF or TF. is computed in the tendon, MTJ, and muscle.

Histological methods.   Three adult mongrel dogs, weighing from 20 to 24 kg each, were killed by intravenous pentobarbital sodium. The diaphragm and ribs of insertion were removed together and placed in a physiological saline solution. We excised portions of the MTJ from the midcostal region of the left hemidiaphragms. Strips 2 in. wide were cut along the muscle fascicles from near the MTJ and through the tendon at their relaxed (unstressed) length. These strips were pinned along their edges to a sheet of cork and placed overnight in a 5% formaldehyde solution. Care was taken to cut the samples 1 cm wide and 1.5 cm from the area where the muscles were pinned. These samples were placed in histological cassettes, cut into longitudinal sections, and stained using a trichrome staining technique. This technique allowed intracellular structures of different architecture and composition to be visibly varied: the muscle fibers and connective tissue of our samples stained red and blue, respectively.

	RESULTS

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In the first protocol, eight position markers were placed in a rectangular configuration (1 cm apart) perpendicular to the axis of the MTJ muscle-tendon interface and defined strain in the muscle, MTJ, and tendon. A representative set of data in Fig. 2 shows the length-tension relationship of muscle tendon uniaxially loaded AF and demonstrates muscle strain > MTJ strain > tendon strain. For example, at tension of 200 g/cm, the strain in these regions was 50, 15, and 5%, respectively. We computed the extension ratio or muscle length as a fraction of unstressed length at tension of 200 g/cm AF and found the extension ratio to be 1.50, 1.15, and 1.05 for the muscle, MTJ, and tendon, respectively. A representative set of data in Fig. 3 shows the length-tension relationship of biaxially loaded diaphragm and also demonstrates muscle strain > MTJ strain > tendon strain. At tension of 200 g/cm, mechanical strains in these regions were 55, 25, and 5%, respectively. The extension ratio at tension of 200 g/cm AF was found to be 1.55, 1.25, and 1.05 for the muscle, MTJ, and tendon, respectively. At low tension, the muscle is more compliant during uniaxial loading (Fig. 2) than during biaxial loading (Fig. 3). For example, at tension of 100 g/cm, the muscle region near the MTJ is passively stretched by 50% during uniaxial stretch, whereas the muscle region is stretched to only 40% at the same level of applied tension. The MTJ however, appears to exhibit similar stress-strain relationships during uniaxial and biaxial loading. For example, at tension of 100 g/cm, the MTJ is stretched to 14% during either uniaxial or biaxial loading. Surprisingly, the tendon near the MTJ exhibits greater strain in response to biaxial loading than in response to uniaxial loading.

View larger version (28K): [in this window] [in a new window]   Fig. 2. Representative set of tension-strain relationships in uniaxially loaded muscle-tendon strips. Strain was computed relative to the unstressed length of the marker spacing. This representative set of uniaxial data shows that muscle strain is greater than the MTJ, which was greater than the tendon strain. At tension of 600 g/cm, the strain in these regions was 5.3, 1.5, and 0.25%, respectively, yielding a compliance ratio of 21.2:6.0:1.0. The J-shaped curve of the MTJ is consistent with previous data on the passive stress-strain relationship of the frog semitendinosis muscle (11).

View larger version (36K): [in this window] [in a new window]   Fig. 3. Representative set of tension-strain relationships in biaxially loaded muscle-tendon strips. Strain was computed relative to the unstressed length of the marker spacing. This representative set of biaxial data shows that stiffness in the direction transverse to the fibers is greater than that along the fibers. The central tendon is essentially inextensible along and transverse to the fibers. The MTJ is slack in the unloaded state. Presumably, during muscle contraction in vivo, the low modulus region of the MTJ length-tension curve could prevent muscle injury during muscle contraction.

View larger version (37K): [in this window] [in a new window]   Fig. 4. Representative set of tension-strain relationships in uniaxially loaded muscle-tendon strips in the direction of muscle fibers for 3 regions in the muscle, 1 region at the MTJ, and 1 region at the tendon. Strain was computed relative to the unstressed length of the marker spacing. In the direction of the muscle fibers, the extensibility of the muscle ranges from 33% at the interface with the tendon to 77% at 1.5 cm away from the junction. Numbers on graph correspond to labeled regions of muscle-tendon strip.

View larger version (24K): [in this window] [in a new window]   Fig. 5. Representative set of tension-strain relationships in uniaxially and simultaneously biaxially stretched muscle strips of the midcostal diaphragm. Markers used to compute mechanical strain were placed midway between origin at the central tendon and insertion on the chest wall. Strain was computed relative to the unstressed length of the marker spacing. These data show that compliance and extensibility in the direction transverse to the fibers are significantly smaller than that along the fibers. Furthermore, the length-tension relationship during biaxial loading is shifted to the left compared with that during uniaxial loading. This indicates that the diaphragm muscle is less extensible during biaxial stretch than during uniaxial stretch.

	DISCUSSION

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Our data demonstrated that 1) the central tendon possesses greater passive stiffness than adjacent diaphragmatic muscle, 2) the diaphragm muscle is anisotropic, whereas the central tendon near the MTJ is essentially isotropic, and 3) a gradient in passive stiffness exists as one approaches the MTJ. Furthermore, our data show that the diaphragm is stiffer during biaxial than during uniaxial loading. Nonlinear length-tension relationships exist both in the AF and in the TF. In the AF, the diaphragm becomes progressively stiffer with increasing extension ratio (the ratio of stressed muscle length to unstressed length). In the TF, the diaphragm becomes inextensible at a relatively low extension ratio.

It is important to note that the data on the muscle length-tension relationships in Fig. 3 are for the muscular region of the MTJ strip, whereas the data in Fig. 5 are for the central region of the muscle between the central tendon and the rib cage. At least in TF, the muscle near the MTJ exhibits less compliance compared with the central region of the diaphragm. During stretching of the diaphragm, an abrupt stop in the lengthening occurs at 25% during biaxial loading. The corresponding stretch of the muscle region near the MTJ occurs at 22%. This confirms a stiffness gradient near the MTJ in TF.

Central tendon possesses greater stiffness than adjacent muscle.   During physiological loads, the central tendon is extremely stiff relative to muscular stiffness along the direction of muscle fibers. Our current results show an increase of costal diaphragmatic muscle stiffness near the MTJ. A sharp transition in stiffness between an inextensible tendon and elastic muscle tissue would result in a condition that could promote muscle-tendon injury at the junction under severe loads. Therefore, in the TF, and relative to the unstressed length of the tissue, one would anticipate essentially zero mechanical strain at the MTJ and almost zero mechanical strain in the muscle fibers near the central tendon. As illustrated in Fig. 6, the individual muscle fibers do not all terminate at a single distinct boundary between muscle and tendon but progress through a zone of transition with gradually increasing proportions of connective tissue. As the muscle transitions into tendon, the increasing proportion of connective tissue establishes a stiffness gradient, thus preventing muscle-tendon injury at the MTJ. The connective tissue near the MTJ is slack in unloaded muscle; therefore, the length-tension relations are a J-shaped curve. Presumably, during muscle contraction in vivo, the low modulus region of the MTJ stress-strain curve could prevent muscle injury at the MTJ during muscle contraction. During contraction, the muscle exerts force along its longitudinal axes. If the diaphragm were extensible in the TF at the MTJ, then as transdiaphragmatic pressure and stress in both directions increase during muscle contraction, the diaphragm would tend to expand in the TF as it contracts along the myofiber direction, and this would create stress concentrations at the MTJ due to tendon inextensibility. The high transverse stiffness of the muscle at the MTJ and inextensibility of the central tendon demonstrated in our data combine a mechanism to eliminate stress concentrations at the muscle-tendon interface, and this mechanism may play an important role in preventing muscle-tendon injury.

View larger version (76K): [in this window] [in a new window]   Fig. 6. Light micrograph of the dog costal diaphragmatic muscle interface (CDI) with the central tendon (CT) showing the major structures. Pleural surface (PL) is attached by collagen strands (CS) to the muscle fibers (MF) and the central tendon. The peritoneum (P) is loosely attached to the abdominal surface of the diaphragm. Individual fibers do not all terminate at a single distinct boundary between muscle and tendon. Instead, there is a zone of transition between the muscle and tendon. In this zone, there is a gradual increase in the fraction of connective tissue to muscle. The cohesion between muscle and tendon, therefore, is expected to be strong because the connective tissue fibers penetrate into the muscle.

Although Chuong et al. demonstrated anisotropy of the central tendon canine diaphragm, they did not specifically investigate the properties of the MTJ (9). Analysis of data from current passive mechanical responses to the various uniaxial and biaxial mechanical loading conditions demonstrates that MTJ behaves as a nonlinear anisotropic tissue with a greater stiffness in the TF than in the AF. Furthermore, the muscle-tendon strip exhibits a nonlinear passive length-tension relationship along the direction of the muscle fibers and becomes progressively stiffer with increasing extension from the unstressed length. As noted by Smith and Loring (14), this nonlinearity is reflected in disproportionate increases in transdiaphragmatic pressure with myofiber elongation at low lung volumes. They reasoned that such nonlinear elastic behavior is presumably related to recruitment phenomena: as extension increases, unstressed fibrous elements at low extension ratio are progressively recruited, contributing their elastic stiffness in parallel at high stiffness. The J-shaped curve of the diaphragmatic MTJ is also consistent with previous data on the passive stress-strain relationship of the frog semitendinosis muscle (11). Furthermore, the Lieber data also showed aponeurosis strain > bone-tendon junction > tendon strain, consistent with the corresponding data of our study. Our data from biaxially loaded muscle-tendon strips show that stiffness in the TF is greater than that in the AF, and the anisotropy is more pronounced in the muscle than in the tendon. Consistent with the results of previous studies on skeletal muscle and tendon, the results of this study specifically establish the anisotropic properties of MTJ.

Stiffness gradient.   Our previous data have shown that the diaphragmatic muscle is relatively inextensible in the TF during physiological loading in supine dogs with average principal strains of 0.015 ± 0.033, 0.004 ± 0.042, and 0.005 ± 0.023 near the central tendon, midway between the insertion, and near the chest wall, respectively (8). The data in the present study demonstrate greater stiffness in the TF of the costal diaphragmatic muscle near the MTJ, and such a large stiffness may result from an increase in the fraction of connective tissue to muscle fibers in that region. As the muscle transitions into tendon near the MTJ, the stiffness increases until it approaches that of the central tendon. This is consistent with the finding of Scott and Loeb (13) in the distal aponeurosis. One would expect a continuity of transverse stiffness across the interface of the MTJ. The relative inextensibility of the costal diaphragmatic muscle in the TF should not cause a discontinuity in the microstress across the interface between the muscle and the tendon, at least in the TF. Our gross anatomic data have shown an average thickness of 0.256 ± 0.037 cm for the dog midcostal costal diaphragm and a thickness of 0.03 ± 0.004 cm for the central tendon (4). The costal diaphragmatic muscle therefore tapers near the MTJ to provide a mechanism for reducing stress concentration that may be generated at the MTJ during physiological or high-resistive mechanical loading. Given the tapering of muscle near the MTJ, one would expect continuous microstresses across the MTJ. This is supported by our data that demonstrate the existence of a stiffness gradient in the transition from muscle to central tendon.

Challenges of in vitro material testing.   Nielsen et al. (12) identified a number of difficulties with in vitro biaxial testing of biological tissue. Among them are 1) the complexity in loading the tissue with hooks, sutures, or support needles, 2) the nonuniform distribution of stress and strain throughout the tissue due to the application of point forces along the edges of the tissue, and 3) the difficulty in creating physiological strain rates and loading conditions. All of these limitations affect the accuracy of in vitro stress-strain analyses. Our biaxial test method is modeled after similar devices with modifications intended to circumvent these problems as best as possible. Biaxial loading by hooks and sutures, as opposed to support needles, reduces any undesirable constraints imposed on the tissue (12). The Saint-Venant's Principle of Mechanics states that two different distributions of force acting on the same portion of a body have essentially the same effects on parts of the body that are sufficiently far from the region of application, provided that these force distributions have the same result. We designed our experiments such that mechanical strains were measured in a small, central region of the tissue, and that renders edge effects negligible (10, 12, 16).

In summary, our study is the first to provide data on physiologically relevant mechanical loading of the diaphragmatic MTJ. Our finding that the central tendon is essentially inextensible in the AF and TF directions is consistent with a mechanism to eliminate stress concentrations at the muscle-tendon interface. Furthermore, this finding supports the possibility that muscle energy expended by fiber shortening during muscle contraction will be utilized in displacing the diaphragm rather than being wasted in deforming the central tendon. In addition, our finding that the diaphragm muscle is anisotropic, whereas the central tendon near the junction is essentially isotropic, provides insight to the understanding of the mechanical behavior of this specialized junction under complex loading conditions. Finally, our finding that there is gradient in passive stiffness that exists AF and TF as one approaches the MTJ provides supporting data that stiffness continuity from the muscle continues through the tendon across the MTJ, a requirement that is fundamental to prevent muscle injury at the MTJ of the diaphragm, possibly during forceful breathing maneuvers.

	GRANTS

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This work was supported by the National Heart, Lung, and Blood Institute Grants HL-072839 and HL-63134.

	ACKNOWLEDGMENTS

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The authors are grateful to Deshen Zhu and R. Mattison for technical assistance.

	FOOTNOTES

 

Address for reprint requests and other correspondence: A. M. Boriek, Baylor College of Medicine, One Baylor Plaza, Dept. of Medicine-Pulmonary Section, Suite 520B, Houston, TX 77030 (E-mail: 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.

	REFERENCES

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This Article Abstract Full Text (PDF) Free Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Hwang, W. Articles by Boriek, A. M. Search for Related Content PubMed PubMed Citation Articles by Hwang, W. Articles by Boriek, A. M.