The method introduced in this study is the first to quantify objectively the morphological complexity of attachment sites. Methods that are currently used to assess attachment site complexity are subjective and difficult to compare statistically (Robb, 1998; Wilczak, 1998). While a clear improvement over previous methods due to its objective and quantitative nature, the method described here does have some issues that are addressed below. This study presents the first data describing the variations in surface complexity of attachment sites. The possible implications of these data and the potential utility of this method for investigating attachment site functional morphology are also discussed.
As with many technologies, laser scan output is subject to a trade-off between file size and resolution. High-resolution 3D scans contain millions of data points and are therefore often too unwieldy to process digitally because they consume excessive amounts of computer memory. However, to be fully informative, fractal analyses require extremely high-resolution images. Since the bones in this study were scanned with overlapping scans from multiple angles, the data collected with this laser scanner are highly detailed to a theoretically unlimited resolution, and the associated files are proportionately large. Data filtration is necessary for storage and processing of these data to be possible. Data filtration removes redundant data points that describe surface locations already described by other points. This reduces computer memory requirements and provides a consistent initial resolution for all scans, enabling comparisons of different scans. However, by definition, fractal analyses examine data at ever increasing levels of magnification. Since data filtration removes many data points, it is possible that in this study this filtration process may have removed informative data. One solution for this issue is not to filter the original scan data, or only to filter it minimally so as to achieve consistent resolutions for all scans. The scans used in this study were filtered as minimally as possible while still allowing data storage and manipulation.
ArcGIS allows the user to visualize a 3D reconstruction in three dimensions, but does not allow measurements to be taken on these 3D images. In ArcGIS, measurements must be taken on two-dimensional representations of the reconstructed shape. Although the image projected on the screen is two-dimensional, all 3D data are maintained in these reconstructions. A viewer's observations of such reconstructed shapes may be thrown off by distortions created by this projection of a 3D surface into a 2D image. It is important therefore for biological shapes that are quantified using this method to have landmarks that are relatively obvious and not defined by their position relative to another feature. For example, the attachment sites quantified here have obvious edges that were clearly demarcated by variations in color (Fig. 2) on the 2D reconstructions and as a result were easily and confidently identified. This method is therefore most useful for quantifying the morphologies of features that are complex but discrete and obvious.
Implications of Results
This study presents the first quantification of variations in surface complexity within attachment sites. Assuming surface morphology is influenced by in vivo muscle activity, this method provides a new way to infer muscle activity and thereby reconstruct behavior. Although a direct relationship has yet to be experimentally proven, a number of researchers have hypothesized mechanisms by which muscle activity may be reflected in attachment site morphology. Mechanical stimuli that lift periosteum from the underlying bone may influence the activity of the osteoprogenitor cells in the periosteum, perhaps by increasing the blood supply to the area (Herring, 1994). Variations in the amount to which bone projects in these attachment sites may reflect variations in periosteal modeling rates at the bone surface. A number of studies have also postulated that the thicknesses and cell shapes of the fibrocartilaginous cell layers in tendinous insertions reflect the types (tensile vs. compressive), gradients, and directions of the stresses the insertions experience (Matyas et al., 1995; Benjamin and Ralphs, 1998 and references therein). For example, the thickness of calcified fibrocartilage in tendinous insertions (Cooper and Misol, 1970; Benjamin et al., 2002) has been hypothesized to reflect the tensile loads experienced by the site (Inoue et al., 1998a). A number of studies have characterized the morphologies and orientations of fibrocartilage cells in the context of their hypothesized mechanical milieux and have supported these theories (Evans et al., 1990; Benjamin et al., 1991, 1992; Inoue et al., 1998a, 1998b; Thomas et al., 1999).
If bony buildup does indicate tensile stresses, a complex profile indicates a greater variance in the magnitudes and directions of stresses experienced along that transect of the site. The general trends observed in this study indicate that most attachment sites experience more varied tensile loads along their peripheries than they do in the middle of their major axes. Another way to describe this phenomenon is that the tensile loads experienced by the attachment sites appear to be more regular or consistent along their proximal-distal and transverse midlines than they are at their peripheries. These results indicate that natural irregularities in the directions or magnitudes of the forces produced by a muscle pull during standing and locomotion are experienced at the peripheries of attachment sites, whereas the centers of attachment sites experience consistent, predictable loads.
The primary exception to this trend is the infraspinatus insertion, which demonstrates no variation in complexity along either of its major axes. The role of this muscle in the maintenance of shoulder stability in quadrupeds (Suzuki, 1995; Dejardin et al., 2001) may limit the variation in its angle of action on its insertion site during a stride. Complexity may not vary within the attachment site because the tensile forces experienced by different parts of the insertion site may not vary significantly throughout a stride.
The gastrocnemius insertion also does not vary in complexity along its vertical (proximal-distal) axis, indicating that the pattern of tensile forces does not vary within this site from proximal to distal. This muscle inserts onto the calcaneal tuberosity, projecting away from the joint to increase the mechanical advantages of the muscle. This morphological arrangement may help produce regular, predictable stresses at the insertion during muscle contraction.
The complexity of the lateral origin of the gastrocnemius muscle also does not vary along its medial-lateral axis and is more complex in the midline of its vertical axis than it is proximally or distally. The center of the gastrocnemius lateral origin appears to experience more varied osteogenic stimuli and perhaps more varied loads than does the distal part of the site. This trend is the opposite of that observed in the other attachment sites examined here. The gastrocnemius lateral origin is the only attachment site in this study in which the muscle fibers attach directly to the bone rather than attaching via a tendon. The pattern of bone complexity observed in this attachment site may actually reflect variations in the patterns of neuromuscular stimulation within the gastrocnemius muscle.
The patterns described here document for the first time quantified variations in morphologies within attachment sites. If tensile stresses do induce bony buildup as has been hypothesized, this method has the potential to bring insight into the biomechanical environments of bones at their sites of muscle and tendon attachments. These insights will contribute to the understanding of the biology of the muscle-bone complex and complement existing models of strain environments in muscle, tendon, and ligament attachment sites (Matyas and Frank, 1988; Inoue et al., 1998a, 1998b), as well as aid in reconstructions of muscle activity and behavior in fossils.
The method described here enables the quantification of variation in morphology within muscle attachment sites or other complex shapes. This tool has great potential for studies of these and other complex morphological surfaces. The use of laser scanners in conjunction with GIS software provides a powerful tool for morphologists. The methods described in this study may provide the first insights into the variations in strain experienced at the junction of muscles or tendons with bone. The ability to quantify complex 3D shapes will allow morphologists to investigate questions that have heretofore remained unexamined because the shapes were simply too complex to measure.