Extracting Cross-Sectional Clinical Images Based on Their Principal Axes of Inertia

Figure 1

Standardized cross section images (CSIs) of the first metatarsal of the right foot. (a) Standardized body coordinate system of the first metatarsal. (b) Center of mass (COM) on the coronal, horizontal, and sagittal plane before positioning. (c) COM on the coronal, horizontal, and sagittal plane after positioning. Equation (1) is used to calculate the COM of the metatarsal. Equations (9)–(11) are used to establish the three sections of the scanned posture (with the COM of the metatarsal on the planes); see panel (a). Equation (1) is used to calculate the COM of the metatarsal and (2)–(7) are applied successively to position the metatarsal; (8) is used to reconstruct the CSIs (panel (b)), while (9)–(11) are used to establish the three sections after they are positioned (with the COM of the metatarsal on the planes); see panel (c). After the first scan, positioning of the first metatarsal was completed in two iterations, first by rotating about the -, - and -axes by 34.25, −10.31, and 22.48 degrees, respectively, and then by 0.09, 0.03, and 0.00 degrees, respectively. Also, after the second scan, positioning of the first metatarsal was completed in two iterations, by rotating about the -, - and -axes first by 38.34, 14.92, and 5.86 degrees, respectively, and then by −0.04, 0.00, and 0.00 degrees, respectively. The COM of the first metatarsal was 69.55, 150.48, and −111.94 mm, in the first scan and 70.30, 91.72, and −168.04 mm in the second scan. The origin of the coordinate system was set at the organ’s COM.

(a)

(b)

(c)