The helical axis of anatomical joints: calculation methods, literature review, and software implementation

Kinematic analysis of forearm rotation using four-dimensional computed tomography

“…This study presented a new approach in which 4-D-CT position data and a circle fit was used to find the axis of rotation rather than calculating the FHA based on a limited number of scan positions. For angular displacements larger than 10°, the error of the FHA analysis is similar to that of the circle fit (Ancillao, 2022; Spoor, 1984; Tay et al., 2008). For smaller angular displacements, which are common for current dynamic imaging studies (Leng et al., 2011; Morishige et al., 2022; Seah et al., 2021), the circle fit outperforms the FHA analysis.…”

“…This study presented a new approach in which 4-D-CT position data and a circle fit was used to find the axis of rotation rather than calculating the FHA based on a limited number of scan positions. For angular displacements larger than 10 , the error of the FHA analysis is similar to that of the circle fit (Ancillao, 2022;Spoor, 1984;Tay et al, 2008). For…”

“…All the 528 FHAs and corresponding angular displacements (ϴ) were calculated from the transformation matrices obtained from each unique combination of two frames within the 4-D-CT scan (Kinzel et al., 1972). This allowed for a comparison between a large angular displacement FHA and a small angular displacement FHA, since a large angular displacement FHA is less prone to error than a small angular displacement FHA (Ancillao, 2022; Spoor, 1984; Tay et al., 2008).…”

“…The FHA describes a single axis in 3-D space along which a body translates and around which it rotates. It is calculated from the repositioning matrix that describes the movement, translations and rotations, of a body between two positions (Ancillao, 2022; Kinzel et al., 1972; Spoor and Veldpaus, 1980). One single FHA could poorly represent movement of the radius during the pronation–supination motion if the radius rotates not only around the ulna but also rotates around and translates along its own axes of inertia.…”

“…One single FHA could poorly represent movement of the radius during the pronation–supination motion if the radius rotates not only around the ulna but also rotates around and translates along its own axes of inertia. Moreover, the FHA approach has been proven to be imprecise for angular displacements of less than 10° (Ancillao, 2022; Spoor, 1984; Tay et al., 2008).…”