The functional role of the membrana ischiopubica in Gallus gallus
The aim of this study was to investigate whether the membrana ischiopubica has the potential to fulfil the criteria of a bending minimization mechanism. In fact, the 2D FE model without (M1) and the 2D FE model with membrana ischiopubica (M2) show major differences in the mechanical loading of the os pubis. In M1, the obtained maximal stress values of both the compressive principal stress (−140 MPa) and the tensile principal stress (223 MPa) are at the level of the cortical bone mechanical strength. The values of the mechanical strength of bone have been measured at −133 to −237 MPa for compressive principal stress and 27–271 MPa for tensile principal stress (Currey, 2002, and references cited therein; Martin et al. 2010, and references cited therein). The wide-ranged values are explained not only by different animals and bones chosen in the studies (Currey, 2002; Martin et al. 2010) but also by differences in experimental settings, such as strain rate (Carter, 1976; Hansen et al. 2008). Unfortunately, the values of bone mechanical strength for the bones of Gallus are not available; however, they most likely lie within these ranges. Nonetheless, the bone mechanical strength is the ultimate stress the material is able to withstand and it seems unlikely that mechanical loading of a bone during ventilation causes stresses at the level of the ultimate stress of the material. The upper limit of the functional stress in bone during everyday activities is more likely linked to the yield stress of bone (Curtis et al. 2011) or to the fatigue strength of bone (Taylor, 2000; Taylor et al. 2003); both values are lower than the ultimate stress of bone. Furthermore, the functional stress in bone is subject to a safety factor; this is not strictly defined in the literature but can lead to a 1.4–6 times reduction of functional stress values in vivo (Biewener, 1993; Robling et al. 2006; Turner, 2006). In addition to that, both compressive and tensile strain levels in a major part of the scapus pubis and parts of the corpus pubis exceed 3000 microstrain (Fig. 3). In the overload range above 3000 microstrain, the bone formation exceeds the bone resorption, leading to net bone mass gain or bone cross-sectional growth (Frost, 2003; Robling et al. 2006; Turner, 2006). In these areas excessive bone remodelling due to overload is expected. However, the levels of functional strain observed in the corpus pubis are above the normally accepted modelling threshold. Thus, loading of the os pubis in M1 does not fully reflect physiological loading conditions of the bone.
In M2, in which the membrana ischiopubica is included, a physiological level of bone loading is re-established by compensating bending loading and subsequently reducing high principal stress values. Here, the maximal compressive principal stress in the os pubis (−12.5 MPa) is much lower than the mechanical strength of bone material and the tensile principal stress (< 0.6 MPa) is virtually absent. It is not sensible to draw conclusions about the safety factor because of the missing data on bone strength in this particular case and limitations of the study discussed below. However, our results for M2 show that the compressive strain levels in most of the os pubis lie between −66.7 and −133 microstrain, corresponding to the lower range of physiological loading. In a bone adapted to everyday loading, e.g. during ventilation and locomotion, strains ranging between 50 and 1500 microstrain are expected (Martin, 2000; Frost, 2003). In this physiological range, the bone resorption equals bone formation. Thus, our results show that the loading during expiration is well suited to maintain the bone structure of the scapus pubis. Nonetheless, the loading of the scapus pubis of Gallus simulated in M2 is in a low physiological range. This shows that the membrana ischiopubica allows for even higher mechanical loading of the os pubis, which can take place during hopping or fluttering, without bringing the bone dangerously close to the ultimate stress.
The compensation of the bending loading in the scapus pubis is explained by the mechanical characteristics of the membrana ischiopubica. The membrana ischiopubica of Gallus is a dense-fibred interosseus membrane (R. Fechner, pers. obs.). The membrana ischiopubica transfers the tensile loading produced by the infrapubic and suprapubic abdominal muscles onto the os ischium and probably os ilium, and at the same time restrains the bending deformation of scapus pubis. With elimination of the tensile principal stresses, the peak compressive principal stresses are reduced and the scapus pubis is strikingly evenly loaded under compression. Additionally, the reduction of the compressive principal stresses on the corpus pubis shows that the mechanical function of the membrana ischiopubica also influences the loading of adjacent structures.
The membrana ischiopubica follows the tension chord principle established by Pauwels (1965). Systematic investigations by Pauwels (1965) showed that bending loading in bones initiates adaptive bone remodelling processes and is minimized in two major ways: (i) using bone remodelling, which leads to the inhomogeneous structure of bones and (ii) using the action of soft tissues or the so-called tension chord principle. Usually, only bone adaptation mechanisms are considered as a bone reaction to the external loading (e.g. Hart, 2001). However, the importance of tension chords cannot be underestimated (Sverdlova & Witzel, 2010; Curtis et al. 2011; Gößling, 2011). In fact, the stimulus to avoid bending loading using both mechanisms culminates in the optimization of bones and muscular architecture for certain loading conditions. Tension chords can be realized by muscles (i.e. active tension chords) or by other soft tissue structures, such as ligaments, tendons, fasciae, and membranes (i.e. passive tension chords). The membrana ischiopubica of Gallus represents a passive tension chord. A passive tension chord has advantages for the musculoskeletal system. Muscle activity is the most costly activity for an organism (Conley & Lindstedt, 2002). Reducing muscle mass by developing membranes or other passive structures can be seen not only as an energy-saving mechanism but also as a weight-saving mechanism (Biewener, 2010). Combining passive soft tissue structures and optimizing bones in terms of minimizing mass has the potential to reduce total energy and weight requirements considerably.
As mentioned above, the arrangement of the collagen fibres in model M2 is not based on histological findings. In model M2, the collagen fibres are oriented perpendicular to the scapus pubis and os ischium, an arrangement characteristic for an uniaxial transmission of tensile forces. The modelled membrane with the uniaxially oriented collagen fibres is close to the behaviour of a real membrane. The tensile deformation of up to 2.1% in the modelled membrana ischiopubica lies within the range expected for a dense-fibred membrane (up to 5%; Schwind, 2009) or a comparable structure, such as a tendon (2–5%; Fung, 1993).
Summarizing, the bending minimization mechanism that controls the loading regime of the os pubis in Gallus is a membranous passive tension chord. The mechanical properties of the membrana ischiopubica allow tensile forces to be transmitted to adjacent bone structures. Thereby, bending loading exerted on the os pubis by contraction of the abdominal muscles during expiration is compensated, and high stresses and strains reduced. This bending minimization mechanism enables the development of delicate bone structures, such as the scapus pubis, despite relatively high mechanical loading.
The mechanical significance of the membrana ischiopubica for the anatomy of the ventral pelvis of Aves
As outlined above, passive tension chords have the advantage of reducing energy and weight requirements. However, the employment of passive tension chords is not possible if active control is required (i.e. joints). In Gallus, the corpus pubis is fused to the os ilium and os ischium and thus a passive structure such as the membrana ischiopubica suffices to oppose the forces exerted on the os pubis. A membrana ischiopubica is present not only in Gallus but is characteristic for most birds. In some neognath birds, the membrana ischiopubica is reduced or lost with the reduction of the fenestra ischiopubica. Nonetheless, it can be expected that the functional role of the membrana ischiopubica of the remaining neognath birds resembles the functional role investigated in Gallus. In ratite birds, this is different. The fenestra ischiopubica is comparatively large. In addition to a dense-fibred membrana ischiopubica covering the greater part of the fenestra ischiopubica (R. Fechner, pers. obs.; Vollmerhaus, 2004), a muscle attaches to the ventral aspect of the ala ischii and the dorsal aspect of the scapus pubis (R. Fechner pers. obs.; McGowan, 1979; Gangl et al. 2004; Picasso, 2010). This muscle, m. obturatorius medialis, functions as an active tension chord opposing the abdominal muscles. Most likely, the membrana ischiopubica assists the m. obturatorius medialis. As yet, the functional reasons for this arrangement in ratite birds has not been identified. Nonetheless, it is interesting to note that there is a relationship between the functional role of the membrana ischiopubica and the organization of m. obturatorius medialis. It appears that the moment m. obturatorius medialis is released from its function as an active tension chord, the origin of this muscle moves to the medial aspect of the ala ischii, as is characteristic for neognath birds. The limitations of a membranous passive tension chord as well as the evolution of the functional role of the membrana ischiopubica within reptiles should be the subject of future studies.