On the anisotropy of the canine diaphragmatic central tendon

We studied the mechanical and anatomical anisotropy of the canine diaphragmatic central tendon (CT). Dumb-bell-shaped strips with effective dimensions of 10 x 2 mm (length x width) were cut from different regions of the canine diaphragmatic CT in two different orientations relative to the direction of neighboring muscle fibers. Specimens sampled with their long axial dimension oriented parallel to the neighboring muscle fibers were named Group-1 and those sampled with an orientation perpendicular to the neighboring muscle fibers were named Group-2. Results from one-dimensional stress-strain and tensile failure strength tests revealed that the CT is a nonlinear, inelastic, and anisotropic material. Group-1 specimens were found to have a higher stiffness, higher failure strength and higher strain energy density at failure than Group-2 specimens. Polarized microscopy showed that multiple sheets of collagen fiber bundles formed an orthogonal network in the tendon. Collagen fiber bundles along Group-1 direction formed parallel trajectory lines connecting the neighboring costal and crural muscles; bundles along Group-2 direction were observed to orient 90 degrees away. At the central apex region of the CT, collagen bundles of Group-1 formed a fan-like trajectory pattern. This collagen network architecture was compared favorably to the trajectories of an approximated principal stress field in the CT due to simulated contractile forces from its adjacent costal and crural muscles. These combined results suggest a structure-function relationship for the anatomical and mechanical anisotropy in the canine diaphragmatic CT.     

Differential costal and crural diaphragm compensation for posture changes

The electromyographic (EMG) activities of the costal and crural diaphragm were recorded from bipolar fine-wire electrodes placed in the costal fibers adjacent to the central tendon and in the anterior portions of the crural fibers in 12 anesthetized cats. The EMG activities of costal and crural recordings were compared during posture changes from supine to head up and during progressive hyperoxic hypercapnia in both positions. The activity of both portions of the diaphragm was greater in the head up compared with supine posture at all levels of CO2; and increases in crural activity were greater than those in costal activity both as a result of changes in posture and with increasing CO2 stimuli. These results are consistent with the concept that diaphragm activation is modulated in response to changes in resting muscle length, and further, that neural control mechanisms allow separate regulation of costal and crural diaphragm activation.     

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

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 approximately 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 approximately 0.15 degrees for both, and, therefore, the shear component of force was approximately 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.     

Absence of regional differences in the size and oxidative capacity of diaphragm muscle fibers

The oxidative capacity and cross-sectional area of muscle fibers were compared between the costal and crural regions of the cat diaphragm and across the abdominal-thoracic extent of the muscle. Succinate dehydrogenase (SDH) activity of individual fibers was quantified using a microphotometric procedure implemented on an image-processing system. In both costal and crural regions, population distributions of SDH activities were unimodal for both type I and II fibers. The continuous distribution of SDH activities for type II fibers indicated that no clear threshold exists for the subclassification of fibers based on differences in oxidative capacity (e.g., the classification of fast-twitch glycolytic and fast-twitch oxidative glycolytic fiber types). No differences in either SDH activity or cross-sectional area were noted between fiber populations of the costal and crural regions. Differences in SDH activity and cross-sectional area were noted, however, between fiber populations located on the abdominal and thoracic sides of the costal region. Both type I and II fibers on the abdominal side of the costal diaphragm were larger and more oxidative than comparable fibers on the thoracic side.     

Computational analyses of mechanically induced collagen fiber remodeling in the aortic heart valve

To optimize the mechanical properties and integrity of tissue-engineered aortic heart valves, it is necessary to gain insight into the effects of mechanical stimuli on the mechanical behavior of the tissue using mathematical models. In this study, a finite-element (FE) model is presented to relate changes in collagen fiber content and orientation to the mechanical loading condition within the engineered construct. We hypothesized that collagen fibers aligned with principal strain directions and that collagen content increased with the fiber stretch. The results indicate that the computed preferred fiber directions run from commissure to commissure and show a strong resemblance to experimental data from native aortic heart valves.     

Shape and tension distribution of the active canine diaphragm

Both diaphragm shape and tension contribute to transdiaphragmatic pressure, but of the three variables, tension is most difficult to measure. We measured transdiaphragmatic pressure and the global shape of the in vivo canine diaphragm and used principles of mechanics to compute the tension distribution. Our hypotheses were that 1) tension in the active diaphragm is nonuniform with greater tension in the central tendon than in the muscular regions; 2) maximum tension is essentially oriented in the muscle fiber direction, whereas minimum tension is orthogonal to the fiber direction; and 3) during submaximal activation change in the in vivo global shape is small. Metallic markers, each 2 mm in length, were implanted surgically on the peritoneal surface of the diaphragm at 1.5- to 2.0-cm intervals along the muscle bundles at the midline, ventral, middle, and dorsal regions of the left costal diaphragm and along a muscle bundle of the crural diaphragm. Postsurgery, a biplane videofluoroscopic system was used to determine the in vivo three-dimensional coordinates of the markers at end expiration and end inspiration during quiet breathing as well as at end-inspiratory efforts against an occluded airway at lung volumes of functional residual capacity and at one-third maximum inspiratory capacity increments in volume to total lung capacity. A surface was fit to the marker locations using a two-dimensional spline algorithm. Diaphragm surface was modeled as a pressurized membrane, and tension distribution in the active diaphragm was computed using the ANSYS finite element program. We showed that the peak of the diaphragm dome was closer to the ventral surface than to the dorsal surface and that there was a depression or valley in the crural region. In the supine position, during inspiratory efforts, the caudal displacement of the dorsal region of the diaphragm was greater than that of the dome, and the valley along the crural diaphragm was accentuated. In contrast, at lower lung volumes in the prone posture, the caudal displacement of the dome was greater than that of the crural region. At end of inspiration, transdiaphragmatic pressure was approximately 6.5 cmH2O, and tensions were nonuniform in the diaphragm. Maximum principal stress sigma(1) of central tendon was found to be greater than sigma(1) of the costal region, and that was greater than sigma(1) of the crural region, with values of 14-34, 14-29, and 4-14 g/cm, respectively. The corresponding data of the minimum principal stress sigma(2) were 9-18, 3-9, and 0-1.5 g/cm, respectively. Maximum principal tension was approximately parallel to the muscle fibers, whereas minimum tension was essentially orthogonal to the longitudinal direction of the muscle fibers. In the muscular region, sigma(1) was approximately 3-fold sigma(2), whereas in the central tendon, sigma(1) was only approximately 1.5-fold sigma(2.).     

Collagen fiber alignment does not explain mechanical anisotropy in fibroblast populated collagen gels

Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.     

Biaxial tensile testing and constitutive modeling of human supraspinatus tendon

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon's two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supraspinatus tendon by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Regional samples were tested under several biaxial boundary conditions while simultaneously measuring the collagen fiber orientations via polarized light imaging. The histograms of fiber angles were fit with a von Mises probability distribution and input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. Samples with a wide fiber angle distribution produced greater transverse stresses than more highly aligned samples. The structural model fit the longitudinal stresses well (median R(2) ≥ 0.96) and was validated by successfully predicting the stress response to a mechanical protocol not used for parameter estimation. The transverse stresses were fit less well with greater errors observed for less aligned samples. Sensitivity analyses and relatively affine fiber kinematics suggest that these errors are not due to inaccuracies in measuring the collagen fiber organization. More likely, additional strain energy terms representing fiber-fiber interactions are necessary to provide a closer approximation of the transverse stresses. Nevertheless, this approach demonstrated that the longitudinal tensile mechanics of the supraspinatus tendon are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers. These results add to the existing knowledge of structure-function relationships in fibrous musculoskeletal tissue, which is valuable for understanding the etiology of degenerative disease, developing effective tissue engineering design strategies, and predicting outcomes of tissue repair.     

Effect of preconditioning and stress relaxation on local collagen fiber re-alignment: inhomogeneous properties of rat supraspinatus tendon

Repeatedly and consistently measuring the mechanical properties of tendon is important but presents a challenge. Preconditioning can provide tendons with a consistent loading history to make comparisons between groups from mechanical testing experiments. However, the specific mechanisms occurring during preconditioning are unknown. Previous studies have suggested that microstructural changes, such as collagen fiber re-alignment, may be a result of preconditioning. Local collagen fiber re-alignment is quantified throughout tensile mechanical testing using a testing system integrated with a polarized light setup, consisting of a backlight, 90 deg-offset rotating polarizer sheets on each side of the test sample, and a digital camera, in a rat supraspinatus tendon model, and corresponding mechanical properties are measured. Local circular variance values are compared throughout the mechanical test to determine if and where collagen fiber re-alignment occurred. The inhomogeneity of the tendon is examined by comparing local circular variance values, optical moduli and optical transition strain values. Although the largest amount of collagen fiber re-alignment was found during preconditioning, significant re-alignment was also demonstrated in the toe and linear regions of the mechanical test. No significant changes in re-alignment were seen during stress relaxation. The insertion site of the supraspinatus tendon demonstrated a lower linear modulus and a more disorganized collagen fiber distribution throughout all mechanical testing points compared to the tendon midsubstance. This study identified a correlation between collagen fiber re-alignment and preconditioning and suggests that collagen fiber re-alignment may be a potential mechanism of preconditioning and merits further investigation. In particular, the conditions necessary for collagen fibers to re-orient away from the direction of loading and the dependency of collagen reorganization on its initial distribution must be examined.     

Passive mechanics of muscle tendinous junction of canine diaphragm.

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.     

Supramolecular order following binding of the dichroic birefringent sulfonic dye Ponceau SS to collagen fibers

The optical anisotropies (linear dichroism or LD and birefringence) of crystalline aggregates of the sulfonic azo-dye Ponceau SS and of dye complexed with chicken tendon collagen fibers were investigated in order to assess their polarizing properties and similarity to liquid crystals. In some experiments, the staining was preceded by treatment with picric acid. Crystalline fibrous aggregates of the dye had a negative LD, and their electronic transitions were oriented perpendicular to the filamentary structures. The binding of Ponceau SS molecules to the collagen fibers altered the LD signal, with variations in the fiber orientation affecting the resulting dichroic ratios. The long axis of the rod-like dye molecule was assumed to be bound in register, parallel to the collagen fiber. Picric acid did not affect the oriented binding of the azo dye to collagen fibers. There were differences in the optical anisotropy of Ponceau SS-stained tendons from 21-day-old and 41-day-old chickens, indicating that Ponceau SS was able to distinguish between different ordered states of macromolecular aggregation in chicken tendon collagen fibers. In the presence of dichroic rod-like azo-dye molecules such as Ponceau SS, collagen also formed structures with a much higher degree of orientation. The presence of LD in the Ponceau SS-collagen complex even in unpolarized light indicated that this complex can act as a polarizer.     

Fiber types and fiber diameters in canine respiratory muscles

In the present study, we measured fiber types and fiber diameters in canine respiratory muscles and examined regional variation within the diaphragm. Samples of eight diaphragm regions, internal intercostals, external intercostals, transversus abdominis, and triceps brachii were removed from eight adult mongrel dogs, frozen, and histochemically processed for standard fiber type and fiber diameter determinations. The respiratory muscles were composed of types I and IIa fibers; no IIb fibers were identified. Fiber composition differed between muscles (P less than 0.0001). Normal type I percent (+/- SE) were: diaphragm 46 +/- 2, external intercostal 85 +/- 6, internal intercostals 48 +/- 3, transversus abdominis 53 +/- 1, and triceps 33 +/- 7. The diaphragm also contained a type I subtype [6 +/- 1% (SE)] previously thought only to occur in developing muscle. Fiber composition varied between diaphragm regions (P less than 0.01). Most notably, left medial crus contained 64% type I fibers. Fiber size also varied systematically among muscles (P less than 0.025) and diaphragm regions (P less than 0.0005). External intercostal fiber diameter was largest (47-50 microns) and diaphragm was smallest (34 microns). Within diaphragm, crural fibers were larger than costal (P less than 0.05). We conclude that there are systematic differences in fiber composition and fiber diameter of the canine respiratory muscles.     

Tensile properties and fiber alignment of human supraspinatus tendon in the transverse direction demonstrate inhomogeneity,nonlinearity, and regional isotropy

A recent study (Lake et al., 2009); reported the properties of human supraspinatus tendon (SST) tested along the predominant fiber direction. The SST was found to have a relatively disperse distribution of collagen fibers, which may represent an adaptation to multiaxial loads imposed by the complex loading environment of the rotator cuff. However, the multiaxial mechanical properties of human SST remain unknown. The objective of this study, therefore, was to evaluate the mechanical properties, fiber alignment, change in alignment with applied load, and structure–function relationships of SST in transverse testing. Samples from six SST locations were tested in uniaxial tension with samples oriented transverse to the tendon long-axis. Polarized light imaging was used to quantify collagen fiber alignment and change in alignment under applied load. The mechanical properties of samples taken near the tendon–bone insertion were much greater on the bursal surface compared to the joint surface (e.g., bursal moduli 15–30 times greater than joint; p<0.001). In fact, the transverse moduli values of the bursal samples were very similar to values obtained from samples tested along the tendon long-axis (Lake et al., 2009). This key and unexpected finding suggests planar mechanical isotropy for bursal surface samples near the insertion, which may be due to complex in vivo loading. Organizationally, fiber distributions became less aligned along the tendon long-axis in the toe-region of the stress–strain response. Alignment changes occurred to a slightly lesser degree in the linear-region, suggesting that movement of collagen fibers may play a role in mechanical nonlinearity. Transverse mechanical properties were significantly correlated with fiber alignment (e.g., for linear-region modulus r_s=0.74, p<0.0001), demonstrating strong structure–function relationships. These results greatly enhance current understanding of the properties of human SST and provide clinicians and scientists with vital information in attempting to treat or replace this complex tissue.     

A quantitative collagen fibers orientation assessment using birefringence measurements: calibration and application to human osteons

Even though mechanical properties depend strongly on the arrangement of collagen fibers in mineralized tissues, it is not yet well resolved. Only a few semi-quantitative evaluations of the fiber arrangement in bone, like spectroscopic techniques or circularly polarized light microscopy methods are available. In this study the out-of-plane collagen arrangement angle was calibrated to the linear birefringence of a longitudinally fibered mineralized turkey leg tendon cut at variety of angles to the main axis. The calibration curve was applied to human cortical bone osteons to quantify the out-of-plane collagen fibers arrangement. The proposed calibration curve is normalized to sample thickness and wavelength of the probing light to enable a universally applicable quantitative assessment. This approach may improve our understanding of the fibrillar structure of bone and its implications on mechanical properties.     

Patterns of neural and muscular electrical activity in costal and crural portions of the diaphragm

To determine whether the central respiratory drives to costal and crural portions of the diaphragm differ from each other in response to chemical and mechanical feedbacks, activities of costal and crural branches of the phrenic nerve were recorded in decerebrate paralyzed cats, studied either with vagi intact and servo-ventilated in accordance with their phrenic nerve activity or vagotomized and ventilated conventionally. Costal and crural electromyograms (EMGs) were recorded in decerebrate spontaneously breathing cats. Hypercapnia and hypoxia resulted in significant increases in peak integrated costal, crural, and whole phrenic nerve activities when the vagi were either intact or cut. However, there were no consistent differences between costal and crural neural responses. Left crural EMG activity was increased significantly more than left costal EMG activity in response to hypercapnia and hypoxia. These results indicate that the central neural inputs to costal and crural portions of the diaphragm are similar in eupnea and in response to chemical and mechanical feedback in decerebrate paralyzed cats. The observed differences in EMG activities in spontaneously breathing animals must arise from modulation of central respiratory activity by mechanoreceptor feedback from respiratory muscles, likely the diaphragm itself.     

Spatial orientation mapping of fibers using polarization‐sensitive second harmonic generation microscopy

In this work, we present a non‐invasive approach to determine azimuth and elevation angles of collagen fibers capable of generating second harmonic signal. The azimuth angle was determined using the minimum of second harmonic generation (SHG) signal while rotating the plane of polarization of excitation light. The elevation angle was estimated from the ratio of the minimal SHG intensity to the intensity when laser polarization and fiber directions were parallel to each other using experimentally determined calibration curve. Pixel‐resolution images of collagen fiber spatial orientation in tendon from bovine leg, chicken leg, and chicken skin were acquired using our approach of SHG polarization‐resolved microscopy. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Respiratory muscle length measured by sonomicrometry

The use of sonomicrometry to study the mechanical properties of the diaphragm in vivo is presented. This method consists of the implantation of piezoelectric transducers between muscle fibers to measure the fibers' changes in length. Ultrasonic bursts are produced by one transducer upon electrical excitation and sensed by a second transducer placed 1-2 cm away. The time elapsed between the generation of the ultrasound burst and its detection is used to calculate the intertransducer distance. Excitation and sampling are done at 1.5 kHz and the output is a DC signal proportional to the length change between the transducers. Neither irreversible injury to the diaphragm nor regional differences within an anatomical part or segment were noted. Measurements were stable within the physiological range of temperature. We measured costal and crural length and velocity of contraction in anesthetized dogs during spontaneous breathing, occluded inspirations, passive lung inflation, and supramaximal phrenic nerve stimulation. We found that shortening during spontaneous breathing was 11 and 6% for crural and costal, respectively. The crural leads the costal in velocity of shortening. Supramaximal stimulation results in a velocity of shortening of 5 resting lengths X s-1. During an occluded inspiration crural shortens as much as in the nonoccluded breath, whereas costal shortens less. During passive lung inflation there is a nearly linear relationship between lung volume and diaphragm length; however, the relationships of chest wall dimensions with diaphragm length are nonlinear and cannot be described by any simple function. Some of the implications of these data on the present understanding of diaphragmatic mechanics are discussed.     

Respiratory changes in diaphragmatic intramuscular pressure

We attempted to measure diaphragmatic tension by measuring changes in diaphragmatic intramuscular pressure (Pim) in the costal and crural parts of the diaphragm in 10 supine anesthetized dogs with Gaeltec 12 CT minitransducers. During phrenic nerve stimulation or direct stimulation of the costal and crural parts of the diaphragm in an animal with the chest and abdomen open, Pim invariably increased and a linear relationship between Pim and the force exerted on the central tendon was found (r greater than or equal to 0.93). During quiet inspiration Pim in general decreased in the costal part (-3.9 +/- 3.3 cmH2O), whereas it either increased or slightly decreased in the crural part (+3.3 +/- 9.4 cmH2O, P less than 0.05). Similar differences were obtained during loaded and occluded inspiration. After bilateral phrenicotomy Pim invariably decreased during inspiration in both parts (costal -4.3 +/- 6.4 cmH2O, crural -3.1 +/- 0.6 cmH2O). Contrary to the expected changes in tension in the muscle, but in conformity with the pressure applied to the muscle, Pim invariably increased during passive inflation from functional residual capacity to total lung capacity (costal +30 +/- 23 cmH2O, crural +18 +/- 18 cmH2O). Similarly, during passive deflation from functional residual capacity to residual volume, Pim invariably decreased (costal -12 +/- 19 cmH2O, crural -12 +/- 14 cmH2O). In two experiments similar observations were made with saline-filled catheters. We conclude that although Pim increases during contraction as in other muscles, Pim during respiratory maneuvers is primarily determined by the pleural and abdominal pressures applied to the muscle rather than by the tension developed by it.     

A structural model for the flexural mechanics of nonwoven tissue engineering scaffolds

The development of methods to predict the strength and stiffness of biomaterials used in tissue engineering is critical for load-bearing applications in which the essential functional requirements are primarily mechanical. We previously quantified changes in the effective stiffness (E) of needled nonwoven polyglycolic acid (PGA) and poly-L-lactic acid (PLLA) scaffolds due to tissue formation and scaffold degradation under three-point bending. Toward predicting these changes, we present a structural model for E of a needled nonwoven scaffold in flexure. The model accounted for the number and orientation of fibers within a representative volume element of the scaffold demarcated by the needling process. The spring-like effective stiffness of the curved fibers was calculated using the sinusoidal fiber shapes. Structural and mechanical properties of PGA and PLLA fibers and PGA, PLLA, and 50:50 PGA/PLLA scaffolds were measured and compared with model predictions. To verify the general predictive capability, the predicted dependence of E on fiber diameter was compared with experimental measurements. Needled nonwoven scaffolds were found to exhibit distinct preferred (PD) and cross-preferred (XD) fiber directions, with an E ratio (PD/XD) of approximately 3:1. The good agreement between the predicted and experimental dependence of E on fiber diameter (R2 = 0.987) suggests that the structural model can be used to design scaffolds with E values more similar to native soft tissues. A comparison with previous results for cell-seeded scaffolds (Engelmayr, G. C., Jr., et al., 2005, Biomaterials, 26(2), pp. 175-187) suggests, for the first time, that the primary mechanical effect of collagen deposition is an increase in the number of fiber-fiber bond points yielding effectively stiffer scaffold fibers. This finding indicated that the effects of tissue deposition on needled nonwoven scaffold mechanics do not follow a rule-of-mixtures behavior. These important results underscore the need for structural approaches in modeling the effects of engineered tissue formation on nonwoven scaffolds, and their potential utility in scaffold design.