Dr. Zumwalt is a research associate in the Department of Biological Anthropology and Anatomy at Duke University. She teaches gross anatomy to medical, graduate, and undergraduate students. She is interested in the influence of external load on bone morphology.
A new method for quantifying the complexity of muscle attachment sites
Article first published online: 21 SEP 2005
Copyright © 2005 Wiley-Liss, Inc.
The Anatomical Record Part B: The New Anatomist
Volume 286B, Issue 1, pages 21–28, September 2005
How to Cite
Zumwalt, A. (2005), A new method for quantifying the complexity of muscle attachment sites. Anat. Rec., 286B: 21–28. doi: 10.1002/ar.b.20075
- Issue published online: 21 SEP 2005
- Article first published online: 21 SEP 2005
- National Science Foundation-BCS. Grant Number: 0209411
- attachment site;
- fractal analysis;
- microscopic anatomy;
Muscle attachment site morphology may have valuable use for reconstructing activity patterns in individuals from historic populations or extinct species. The skeletal locations where muscles and tendons attach are morphologically very complex, and variations in this morphology may reflect stresses experienced by these attachment sites as a result of muscular contractions. However, existing methods for assessing attachment site complexity are qualitative and subjective. This article describes a new method for quantifying attachment site complexity in which attachment sites are scanned with a 3D laser scanner and the morphological complexities of their surfaces are quantified using fractal analysis. The method described here documents the complexity at specific transects along six limb attachment sites in adult female sheep (Ovis aries), and variations in complexity within attachment sites are explored. Overall trends indicate that most of the attachment sites examined here are more complex at their peripheries than at their centers, indicating that these sites experience more varied loads at the peripheries of the tendon attachments. Exceptions to this trend are noted and all functional implications are discussed. This method provides the first opportunity to explore variations in morphological complexity within attachment sites. Assuming a relationship between tensile strains and bony morphology exists, this method provides a new tool to explore the strain environments of muscle attachment sites. Anat Rec (Part B: New Anat) 286B:21–28, 2005. © 2005 Wiley-Liss, Inc.
Biological shapes are frequently very complex. Standard linear or area measurements are often not sufficient to quantify their morphologies entirely. The locations on the skeleton where muscles and tendons attach to bone are one such example of a complex biological feature. The morphologies of these surfaces, also called entheses (Benjamin et al., 2002), are commonly believed to reflect in vivo muscle activity and have been employed for the reconstruction of activity from ancient bones or fossils (Robb, 1994; Hawkey and Merbs, 1995; Kennedy, 1998; Wilczak, 1998). However, the relationship between muscle activity and attachment site morphology has not been thoroughly tested (Zumwalt, 2005). One reason that the functional morphology of muscle attachment sites is still poorly understood is that these features are very difficult to quantify objectively. Attachment sites are extremely complex three-dimensional structures, and to quantify their morphology thoroughly, a method must be able to identify and measure a range of morphologies, from small and flat features to large and rotund ones, and complex combinations of both.
One feature that has often been used to reconstruct the in vivo activity of muscles is the three-dimensional complexity of the surface at the site of attachment (Angel et al., 1987; Kelley and Angel, 1987; Laughlin et al., 1991; Hawkey and Merbs, 1995; Wilczak and Kennedy, 1997; Kennedy, 1998; Robb, 1998; Wilczak, 1998; Capasso et al., 1999; Imber and Aiello, 2001). Current methods for documenting the complexity of muscle attachment sites use the qualitative appearance of a site to assign it to one of a number of predefined categories that are defined based on surveys of the normal range of variation in human attachment site morphology (Hawkey, 1988; Robb, 1994; Hawkey and Merbs, 1995). These methods, while useful for describing complex morphologies, produce challenging statistical problems (Robb, 1998; Stirland, 1998; Wilczak, 1998) and are inherently subjective, making them inadequate for rigorous investigations of attachment site functional morphology.
This study describes a new method to quantify the complexity of attachment sites objectively. In this method, a 3D laser scanner is used to capture the entirety of the complex surface. Laser scanners provide the appropriate technology for collecting surface morphology data from localized areas of bone surfaces because they provide the appropriate resolution and work envelope size for these features (Ungar and Williamson, 2000). The method presented here is an expansion of one used by Ungar and Williamson (2000) to document primate dental wear patterns. In their method and in the current one, laser scans of complex biological surfaces are viewed and analyzed in Geographic Information Software (GIS), which allows the user to visualize a scan in three dimensions, move it freely along or rotate it about any axis, and measure complex aspects of its shape.
In this study, the attachment sites' surface complexity is quantified by assessing the fractal nature of these surfaces. Fractal analysis quantifies the degree to which a measured value changes when assessed with varying degrees of precision. Another way to look at this concept is that fractal analyses describe how much true detail is missed when the object of interest is measured with an imprecise measuring tool (Fig. 1). This method for the first time allows variations in complexity to be quantified within and across attachment sites.
MATERIALS AND METHODS
The complexities of six limb attachment sites were quantified in 20 adult female sheep (Ovis aries). All of the attachment sites examined in this study are clearly observable on sheep bones and the identities of the attaching muscles were confirmed by dissection (Zumwalt, 2005). The following attachments were examined in this study: the insertion of the infraspinatus muscle on the humeral head; the insertion of the triceps brachii muscle on the olecranon process of the ulna; the insertion of the biceps brachii muscle onto the radial tuberosity of the radius; the insertion of the patellar tendon to the tibial tuberosity on the proximal tibia; the lateral origin of the gastrocnemius muscle from the posterior distal femur; and the insertion of the gastrocnemius tendon onto the calcaneal tuberosity of the calcaneus (the flexor digitorum superficialis muscle also partially attaches to this site).
The surfaces of the attachment sites were scanned with a Surveyor Model 810 laser scanner outfitted with an RPS-120 laser sensor (Laser Design, Minneapolis, MN). Data collection was managed by Surveyor Scan Control (SSC) software (Laser Design), which integrates all scan data for digital reconstruction of the surface. Geomagic Studio Reverse Engineering Software (Raindrop Geomagic, Research Triangle Park, NC) handled data filtering and reverse engineering of the digital surface. The laser functions by moving 480 beams of light along the surface of an object, bouncing them off the specimen and viewing them with two sensors. The information received by the sensors is then reconstructed via triangulation to its location in space relative to the scanner. As the distance between the laser and the specimen can vary due to variations in the height of the specimen, the point spacing (resolution) of a single scan can vary, ranging from 0.023 to 0.027 mm, with a single point accuracy of 0.00635 mm (RPS laser specifications; Laser Design).
Shapes that are too large or complex to be fully scanned from one orientation (e.g., the triceps brachii insertion, which wraps around the olecranon process) were scanned in multiple orientations. In these cases, small spheres were maintained in the same positions relative to the surface of interest and were also scanned in every orientation. The SSC software then used triangulation of these known constant shapes to reconstruct the location of the scan in space and merge the scans from each orientation into a single 3D reconstruction of the bone.
To remove redundant points, reduce file size, and maintain a constant point density in the point cloud, all scans were passed through a 3D Proximity Filter (included in the Geomagic software) before analysis. This filter removed points until the minimum distance between any two points in 3D space was 0.025 mm. After filtering, the coordinate space of the scans was visually adjusted so the major axes of the attachment sites were aligned to the axis of soft tissue attachment.
Finally, the data were exported to ArcGIS 8.3 (ESRI, Redlands, CA). The 3D scan data output from the laser scanner had to be reformatted into a new file type to be readable by ArcGIS. The script of the Java program used to reformat the laser scanner's ASCII output into text files was written by the author and is freely available by request. In ArcGIS, these data were reconstructed into 3D point clouds using the x-, y-, z-coordinate data using an Inverse Distance Weighting (IDW) interpolation technique, which predicts the value at an unmeasured location by weighting the values of surrounding measured points based on their proximity to the location in question (Minami, 2000). The cell size (resolution) of each interpolated raster was determined by the largest cell size of that scan's raw data. These analyses therefore are unable to investigate the complexity of osteological structures (e.g., Sharpey's fibers) that are smaller than this cell size (cell sizes of attachment site reconstructions in this study: 0.0794 ± 0.016 mm2).
Defining the Attachment Site
The original laser scans include not only the attachment site of interest, but also some of the surrounding bone. Noninsertion bone was included in the scans to ensure that the entirety of the attachment site was scanned. Additionally, the noninsertion morphology provided landmarks for orienting the attachment site scans in anatomical position. Once the 3D reconstructions were created from the point clouds, however, it was necessary to isolate the attachment site from the noninsertion bone for analysis. In all quantitative analyses of muscle attachment sites, the edges of the sites must be accurately defined. The accuracy of this step is determined by the observer's ability to differentiate attachment site from noninsertion bone. The attachment sites examined here have clear edges and delineation of these edges in two dimensions on a computer screen was straightforward and confirmed by an error study (Zumwalt, 2005). Recognition of the edges of these attachment sites was not significantly more difficult using reconstructed surfaces in ArcGIS than it was when using the real bone. However, future studies using this method should bear in mind the importance of this step when choosing appropriate surfaces to analyze.
The interpolated surfaces are displayed in two dimensions using map projection algorithms that are part of the ArcGIS package. In this study, the reconstructions of the attachment sites were displayed in anatomical position. Ranges of elevation (Z) values are assigned colors so scans appear as color-coded topographical maps (Fig. 2A). Variations in height appear as variations in color. To isolate the attachment site surface from the noninsertion bone, the edge of the attachment site was defined by the observer on the reconstruction (Fig. 2B). The region of interest was outlined using a digitization tool while using the real bone as a reference to ensure accuracy. Bones were held by hand in the same orientation in which they were rendered on the screen and real variations in bone elevation and contour were compared to the variations indicated by the color variations in the rasters. A new raster was then interpolated from the data within the digitized attachment site borders (Fig. 2C). All further analyses were performed on these raster reconstructions of the attachment sites themselves.
Fractal analyses were performed on profiles extracted along transects of the attachment site along two perpendicular axes of the attachment site's surface, one corresponding to the longitudinal axis of the soft tissue attachment (Fig. 3). For all attachment sites included in this study, this axis corresponds to the proximodistal axis of the site. Three profiles were extracted at equidistant locations along the maximum length of each axis. The point spacing of each extracted profile was equal to the length of the profile divided by the resolution of the 3D reconstruction. The fractal dimensions of these profiles therefore indicate the complexity of the bone surface along the axis of soft tissue attachment and that perpendicular to that axis. This method allows for assessments of variations in surface complexity within attachment sites.
The fractal dimensions of the curves were analyzed using Benoit 1.3 fractal analysis software (TruSoft International, St. Petersburg, FL). The algorithm used in this study is called the rescaled range R/S analysis method (see Fig. 4 caption for a description). This algorithm is designed to assess the fractal natures of self-affine curves with equal sampling intervals (i.e., the points that make up the extracted profile are equally spaced) such as the profiles used in this study. The outputs of these analyses are therefore comparable between different data sets (Benoit Fractal Analysis System help files; TruSoft International). Larger fractal dimensions indicate more complex profiles. Wilcoxon rank-sum tests were used to compare the fractal dimensions of different locations on the same attachment sites.
To test the validity of the algorithm and software used here to assess fractal dimensions, six lines with known relative complexities were generated (Fig. 5). Lines 1–3 were created using a self-affine trace generator (included with the Benoit 1.3 software), which creates profiles with known fractal dimensions. Lines 4–6 are known Euclidean shapes: line 4 is a repeating series of lines with 45° and −45° slopes, and lines 5 and 6 are both sine curves. While the exact fractal dimensions of lines 4–6 were not known before this test, the fact that they are Euclidean shapes dictates that their fractal dimensions be less than or equal to one.
|Line 1||Line 2||Line 3||Line 4||Line 5||Line 6|
|Description:||Fourier (H = 0.7)||Fourier (H = 0.5)||Fourier (H = 0.3)||45° Slopes||Sine Wave (one peak)||Sine Wave (3 peaks)|
The fractal dimensions of mathematically created profiles are presented in Table 1. The calculated fractal dimensions of these mathematically generated lines indicate that the algorithm used here provides accurate assessments of fractal complexity. Lines 1–3 were generated with known fractal dimensions (D) of 1.3, 1.5, and 1.7, respectively. The calculated fractal dimensions are exactly the same as these expected values after they are rounded to the same decimal point. The fractal dimensions of lines 4–6 were expected to be less than or equal to one due to the Euclidean nature of their shapes. This prediction was upheld when the fractal dimensions of these lines were calculated to be 0.108, 0.468, and 0.463, respectively. The algorithm used in this study is therefore appropriate for calculating the fractal dimensions of the profiles examined in this study.
The fractal dimensions of profiles extracted parallel and perpendicular to the axes of soft tissue attachment in each attachment site are presented in Tables 2 and 3, respectively. Larger fractal dimensions (D) indicate more complex profiles. The results of Wilcoxon rank-sum tests comparing the fractal complexities of the different locations are also presented.
|25% (medial or anterior)||50% (sagittal midline)||75% (lateral or posterior)||Significant differences (Wilcoxon rank-sum, α = 0.05)|
|Infraspinatus||1.607 (±0.17)||1.605 (±0.15)||1.614 (±0.16)||n.s.|
|Triceps brachii||1.557 (±0.14)||1.465 (±0.15)||1.532 (±0.15)||25% > 50%; 75% > 50%|
|Biceps brachii||1.718 (±0.11)||1.724 (±0.17)||1.780 (±0.12)||75% > 50%|
|Quadriceps femoris||1.642 (±0.12)||1.514 (±0.15)||1.570 (±0.18)||25% > 50%; 25% > 75% (p = 0.062)|
|Gastrocnemius lateral origin||1.452 (±0.14)||1.495 (±0.11)||1.470 (±0.13)||n.s.|
|Gastrocnemius insertion||1.434 (±0.19)||1.276 (±0.10)||1.400 (±0.19)||25% > 50%; 75% > 50%|
|25% (proximal)||50% (middle)||75% (distal)||Significant differences (Wilcoxon rank-sum, α = 0.05)|
|Infraspinatus||1.646 (±0.16)||1.590 (±0.13)||1.575 (±0.14)||n.s.|
|Triceps brachii||1.493 (±0.20)||1.411 (±0.13)||1.388 (±0.21)||25% > 50%|
|Biceps brachii||1.750 (±0.18)||1.560 (±0.16)||1.600 (±0.13)||25% > 50%; 25% > 75%|
|Quadriceps femoris||1.600 (±0.18)||1.392 (±0.14)||1.635 (±0.23)||25% > 50%; 75% > 50%|
|Gastrocnemius lateral origin||1.501 (±0.18)||1.569 (±0.19)||1.408 (±0.17)||50% > 75%|
|Gastrocnemius insertion||1.458 (±0.21)||1.488 (±0.15)||1.429 (±0.17)||n.s.|
There are several general trends that seem to hold true, with some interesting exceptions. In general, attachment sites seem to be more complex at their peripheries than they are at their centers. Profiles extracted along the longitudinal axis of soft tissue attachment tend to be smoother (have lower values for D) along their midlines than those extracted along the medial or lateral (or anterior or posterior) parts (Table 2). This trend is true for the triceps brachii, biceps brachii, and gastrocnemius insertions. An exception to this trend is this quadriceps femoris insertion, which is more complex medially than it is laterally or along its midline. Profiles that run perpendicular to the longitudinal axis of soft tissue attachment also seem to be significantly smoother along the proximal-distal midline (50% of maximum height) of the attachment site than are those that are extracted from the superior or inferior parts of the sites (Table 3). Specifically, the triceps brachii, biceps brachii, and quadriceps femoris insertions are all more complex proximally and the quadriceps is also more complex distally than these insertions are in their proximal-distal midlines.
Attachment sites that do not follow either of these trends are the infraspinatus insertion, which exhibits no significant variation in complexity along either of its major axes, and the gastrocnemius insertion, which also does not vary in complexity from proximal to distal. Additionally, the gastrocnemius lateral origin does not vary in complexity from medial to lateral and is actually more complex in the center of its proximodistal axis than it is distally, which is the opposite pattern than that observed in the other attachment sites. The potential implications of these trends and their exceptions are discussed below.
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.
I am grateful to Dr. Suzanne Strait for the use of her laser scanner and to Dr. Andrew Biewener for providing animal housing at the Concord Field Station throughout the course of this experiment. I am also grateful to Dr. Christopher Ruff for extensive advice in planning this project and to Dr. Peter Ungar for invaluable advice about the use of the ArcGIS software. Dr. Daniel Schmitt and two anonymous reviewers provided insightful and invaluable comments on an earlier version of this manuscript. This project was supported by the National Science Foundation-BCS (0209411), a Journal of Experimental Biology Traveling Fellowship, and Sigma Xi.
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