Tibia Coordinate System¶
The tibia’s fixed coordinate system is defined using data reported during experimental setup and the transform (\(T_{Im\_Sen}\)) defined during the registration for the tibia (Registration). The file data-MC-oks003/State.cfg
contains the transform that is used to define the tibia’s fixed coordinate system with respect to the tibia’s position sensor. Below you can see the relevant data from data-MC-oks003/State.cfg
with unused data removed:
[Knee JCS]
T_Sensor2_RB2 = "<size(s)=4 4> 0.5805398524 0.7813549675 0.2290368848 0.0748743152 0.0563481400 0.2420640867 -0.9686226639 -0.0471447919 -0.8122797344 0.5752298608 0.0964999501 -0.0152677242 0.0000000000 0.0000000000 0.0000000000 1.0000000000"
Where T_Sensor2_RB2
is converted to a 4x4 matrix. The first three rows in the last last column of T_Sensor2_RB2
are the translations for the transform, and these values are multiplied by 1000 to convert from meters to millimeters.
Given that oks003 is a left knee specimen, \(T_{Sensor2\_RB2}\) is reflected about the x-axis, which is shown below. The reflection of \(T_{Sensor2\_RB2}\) is \(R_{Sensor2\_RB2}\) (note that this is not needed for a right knee specimen).
Next the transform from the MR image’s global coordinate system to the tibia’s fixed coordinate system in the MR image (\(T_{Im\_RB2}\)) is defined. \(T_{Im\_Sen2}\) (which is determined from registration of rigid body 2 fiducial points) is multiplied by \(R_{Sensor2\_RB2}\)
\(T_{Im\_RB2}\) can be used to define the tibia’s fixed coordinate system in the knee model using the SimVitro convention, where the positive direction anterior-posterior axis points posteriorly. To match the convention used by this lab, the fixed tibial coordinate system defined by \(T_{Im\_RB2}\) is rotated 180 degrees about the fixed tibia’s z-axis. This defines the positive direction along the anterior-posterior axis as pointing anteriorly.
The last row in \(S_{Im\_RB2}\) is neglected, and the columns are used to define the axes of the fixed tibial coordinate system and its origin.