User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide - Gait Analysis II - 1
CX1 USER GUIDE - COMPLETE.doc 26/04/04 68/162
Derivation of Segment Definitions from Marker Positions
In every case, the dynamic representation of a segment follows from vector re-
constructions based on a minimum set of three points. For the pelvis we first obtain the
orientation of the local co-ordinate frame (hereafter referred to as ‘Embedded Vector
Basis’: EVB) from the available marker set and obtain its reference points using local
offsets. For the remaining limb segments we first obtain the reference points by vector
constructions, then the local EVBs are derived from those. The EVBs are required for the
subsequent calculation of Euler Angles.
Pelvic Landmarks
The derivation for the pelvis model depends, to a certain extent, on whether the
acquisition is unilateral or bilateral, although the underlying model is essentially the same.
The model assumes the Pelvic Frame is strapped to the patient so that it is aligned with
the PSIS/ASIS plane of the pelvis. With the frame correctly fitted, the sacrum lies just
below the base of the sacral wand, but note that the sacral wand marker is NOT used to
determine the position of the sacrum; it merely contributes information about the pelvic
plane. We obtain the orientations of the co-ordinate frame axes before applying local
offsets for the reference points.
Unilateral:
In the unilateral case the orientation of the local x axis is defined by the line joining Psis
marker to Asis marker:
u
x
= U
x
(M
asis
- M
psis
)
where u
x
is a unit vector obtained from the normalization function U
x
applied to the Psis
and Asis position vectors. (Note: The Psis marker must line up with P.S.I.S. as this is,
effectively, the pelvic origin. The ASIS marker, however, does NOT determine the
location of the ASIS and should be positioned further forward as it is used only for axial
orientation.)
The local y axis, u
y
, is obtained using a Gram-Schmidt procedure (denoted by GS
y
) with
the Sacral Wand marker and u
x
(already obtained):
u
y
= U
y
(u
x
, M
sac
)
The local z axis, u
z
, is the normalized vector (‘cross’) product of u
x
and u
y
:
u
z
= U
z
(u
x
, u
y
)
The Sacrum ref.pt. is now obtained as a local lateral offset from the Psis marker. The
offset is half of the pelvic width, W, (Patient Data) plus a fixed adjustment of 20mm to
compensate for the external siting of the markers:
P
sac
= M
psis
+ (20 + ½W)u
y
The ASIS ref.points are similarly offset from the Psis marker by a distance of 1 pelvic
depth, d, (Patient Data) in the local anterior direction on both sides of the pelvis with
appropriate lateral offsets:
P
asis1
= M
psis
+ du
x
+ 20u
y