Page 209 - Advances in Biomechanics and Tissue Regeneration

204 10. DETERMINATION OF THE ANISOTROPIC MECHANICAL PROPERTIES OF BONE TISSUE

The dimensional information of I s is used to define the size of an image containing the family of parallel lines with ι ¼ 0
degrees. Fig. 10.2A represents an example of an image containing a family of parallel lines I ι , in this case, with ι ¼ 0
degrees. Counting the interceptions of those parallel lines with changes of phase of RVE, represented by the bound-
aries of the I s , it is possible to obtain the orientation-dependent feature.
Rotating the family of parallel line images with ι between 0 and 180 degrees using a defined angle increment, and
then counting the interception of the family of parallel lines with I s , it is possible to obtain the ODF of the I s . The gen-
erated data for ι between [180,360] degrees is a [0,180] degrees data repetition because the orientation-dependent
feature is not influenced by the direction. For example, Fig. 10.2 represents the rotation of I ι between 0 and 180 degrees
with a ι increment of 45 degrees.
To better understand how the ODF data are acquired using I s and I ι , Figs. 10.3–10.5 are presented. Each image makes
reference to one of the images presented in Fig. 10.1,with ι between 0 and 180 degrees, using an increment
of 45 degrees. In each one of the images, five pixel colors—black, blue, cyan, red, and pink—are presented, as a result
of the combination of multiple image information. The blue pixels represent the corresponding white pixels from the I s
image. The black pixels represent the background of the I s image. This information is constant in each set of images

(A) (B) (C) (D) (E)

FIG. 10.2 Images of parallel line rotation I ι with an angle increment of 45 degrees, within the interval of ι ¼ 0,180degrees . (A) I pl 0 degrees; (B) I pl
45 degrees; (C) I pl 90 degrees; (D) I pl 135 degrees; (E) I pl 180 degrees.

(A) (B) (C) (D) (E)
FIG. 10.3 Grid lines rotation interceptions of Fig. 10.1A. (A) 0 degrees; (B) 45 degrees; (C) 90 degrees; (D) 135 degrees; (E) 180 degrees.

(A) (B) (C) (D) (E)
FIG. 10.4 Grid lines rotation interceptions of Fig. 10.1B. (A) 0 degrees; (B) 45 degrees; (C) 90 degrees; (D) 135 degrees; (E) 180 degrees.

(A) (B) (C) (D) (E)
FIG. 10.5 Grid lines rotation interceptions of Fig. 10.1C. (A) 0 degrees; (B) 45 degrees; (C) 90 degrees; (D) 135 degrees; (E) 180 degrees.

I. BIOMECHANICS