Figure 1.
Overview illustrating the boundary conditions.
The Neumann boundary conditions imposed on the different regions of the muscle surface to solve the Laplace equation (1) are shown. The full lines represent the surface of the muscle belly, while the tendon attachment regions are indicated by dashed lines. The potential gradients normal to the surface are denoted by , while
indicates the area of the tendon attachment surfaces.
Figure 2.
2D examples of calculated fascicle trajectories.
These results obtained in 2D synthetic muscle geometries demonstrate the feasibility for complex shapes that are representative for anatomical muscle architectures: a simple pennate structure (a), long and narrow attachment as in the rectus femoris muscle (b), asymmetric broad attachments as in the biceps femoris muscle (c), a deltoid-like architecture (d) and a representation of the pectoral diaphragm (e).
Figure 3.
Results for the 3D anatomical example of the human tibialis anterior muscle.
The muscle in this example is located in the lower left leg, anterior to the tibia and fibula. On the left, a sampling of the generated fascicle tracts is shown in an anterior view of the muscle. The origin (proximal) and insertion (distal) attachments are indicated in green and blue respectively. The insertion tendon (blue) divides the muscle in a deep and superficial compartment, of which the fascicle tracts are shown in red and yellow color tones respectively. The color tones are only used for purpose of enhancing the visual contrast. The fascicle tracts are shown in an anterolateral view for the two compartments separately in the middle column. On the right, the distributions of the calculated pennation angles and fascicle tract lengths are shown on the opposing sides of the insertion tendon surface in a similar fashion as in [17]. The upper and lower rows show the results for the superficial and deep compartments respectively. The anatomical orientations (ant = anterior, post = posterior, dist = distal, prox = proximal) are indicated for the superficial surface in the upper row and are the same for the deep surface.
Figure 4.
Generated fascicle trajectories in 3D anatomical examples of skeletal muscles.
In each muscle, the origin (proximal) and insertion (distal) attachment regions are shown in green and blue respectively. For sake of visibility, only samplings of fascicle tracts on the muscle surface are shown. The different colors of the fascicle tracts are only for purpose of visual contrast.