Target Outcome
The overall goal of this specification is to provide coordinate systems for each registration marker sets on femur, tibia, and patella with the intention to allow transformation between joint testing and anatomical imaging coordinate systems. In this regard, the goals are
- Establish the relationship between registration marker coordinate systems (of femur, tibia, and patella) and the coordinate system of motion capture and joint testing (Optrotrak global coordinate system)
- Establish the relationship between registration marker coordinate systems (of femur, tibia, and patella) and anatomical imaging coordinate system (MRI global coordinate system)
Prerequisities
Infrastructure
- ["Infrastructure/ExperimentationMechanics"]
- ["Infrastructure/ExperimentationImaging"]
Previous Protocols
- ["Specifications/Specimens"]
- ["Specifications/SpecimenPreparation"]
- ["Specifications/ExperimentationAnatomicalImaging"]
- ["Specifications/ExperimentationJointMechanics"]
Procedures
Obtaining Location of Registration Marker Centers
The registration markers are spherical objects. The boundaries of these spheres will be digitized from magnetic resonance imaging and during joint testing using a digitizing probe, see Previous Protocols above. More than 10 points are expected to be acquired for each registration marker for a given experimentation modality. The location of a given registration marker will be obtained from a sphere fit to the locations of these points. A Python script will allow the following input/output relationship in the coordinate system of measured points.
- input
coordinates of n locations on a given registration marker (n > 10)
- output
center and radius of sphere (x, y, z, r) that best represents the spherical distribution of n locations
Transformation Matrices
Femur
It is assumed that all the registration marker locations described below are obtained following the protocol described above. Variables to establish the transformation matrix between femur and joint testing coordinate systems are:
latex($p_1^O$): center of the central/posterior registration marker on the femur in Optotrak global coordinate system
latex($p_2^O$): center of the lateral registration marker on the femur in Optotrak global coordinate system
latex($p_3^O$): center of the medial registration marker on the femur in Optotrak global coordinate system
latex($o_F$): origin of the femur fixed registration marker coordinate system in Optotrak global coordinate system
latex($u_F$): x-axis of the femur fixed registration marker coordinate system in Optotrak global coordinate system
latex($v_F$): y-axis of the femur fixed registration marker coordinate system in Optotrak global coordinate system
latex($w_F$): z-axis of the femur fixed registration marker coordinate system in Optotrak global coordinate system
latex($T_{OF}$): transformation matrix from femur fixed registration marker coordinate system to Optotrak global coordinate system
The transformation matrix between femur and joint testing coordinate system can be obtained as:
Variables to establish the transformation matrix between femur and imaging coordinate systems are:
latex($p_1^I$): center of the central/posterior registration marker on the femur in anatomical imaging coordinate system
latex($p_2^I$): center of the lateral registration marker on the femur in anatomical imaging coordinate system
latex($p_3^I$): center of the medial registration marker on the femur in anatomical imaging coordinate system
latex($o_F$): origin of the femur fixed registration marker coordinate system in anatomical imaging coordinate system
latex($u_F$): x-axis of the femur fixed registration marker coordinate system in anatomical imaging coordinate system
latex($v_F$): y-axis of the femur fixed registration marker coordinate system in anatomical imaging coordinate system
latex($w_F$): z-axis of the femur fixed registration marker coordinate system in anatomical imaging coordinate system
latex($T_{IF}$): transformation matrix from femur fixed registration marker coordinate system to anatomical imaging coordinate system
The transformation matrix between femur and imaging coordinate system can be obtained by following the steps already outlined above.
Tibia
It is assumed that all the registration marker locations described below are obtained following the protocol described above. Variables to establish the transformation matrix between tibia and joint testing coordinate systems are:
latex($p_1^O$): center of the central/posterior registration marker on the tibia in Optotrak global coordinate system
latex($p_2^O$): center of the lateral registration marker on the tibia in Optotrak global coordinate system
latex($p_3^O$): center of the medial registration marker on the tibia in Optotrak global coordinate system
latex($o_T$): origin of the tibia fixed registration marker coordinate system in Optotrak global coordinate system
latex($u_T$): x-axis of the tibia fixed registration marker coordinate system in Optotrak global coordinate system
latex($v_T$): y-axis of the tibia fixed registration marker coordinate system in Optotrak global coordinate system
latex($w_T$): z-axis of the tibia fixed registration marker coordinate system in Optotrak global coordinate system
latex($T_{OT}$): transformation matrix from tibia fixed registration marker coordinate system to Optotrak global coordinate system
The transformation matrix between tibia and joint testing coordinate system can be obtained through similar calculations conducted for femur above. Variables to establish the transformation matrix between tibia and imaging coordinate systems are:
latex($p_1^I$): center of the central/posterior registration marker on the tibia in anatomical imaging coordinate system
latex($p_2^I$): center of the lateral registration marker on the tibia in anatomical imaging coordinate system
latex($p_3^I$): center of the medial registration marker on the tibia in anatomical imaging coordinate system
latex($o_T$): origin of the tibia fixed registration marker coordinate system in anatomical imaging coordinate system
latex($u_T$): x-axis of the tibia fixed registration marker coordinate system in anatomical imaging coordinate system
latex($v_T$): y-axis of the tibia fixed registration marker coordinate system in anatomical imaging coordinate system
latex($w_T$): z-axis of the tibia fixed registration marker coordinate system in anatomical imaging coordinate system
latex($T_{IT}$): transformation matrix from tibia fixed registration marker coordinate system to anatomical imaging coordinate system
The transformation matrix between tibia and imaging coordinate system can be obtained by following the steps outlined for the femur, see above.
Patella
The following information should be available from CAD drawing of the patella registration marker assembly:
latex($p_{Di}^C$): divot coordinates on patella registration marker assembly in CAD coordinate system (i = 1 to 12)
latex($p_1^C$): center of the central/superior registration marker on the patella in CAD coordinate system
latex($p_2^C$): center of the lateral registration marker on the patella in CAD coordinate system
latex($p_3^C$): center of the medial registration marker on the patella in CAD coordinate system
The location of divot coordinates should be measured during specimen preparation:
latex($p_{Di}^O$): divot coordinates on patella registration marker assembly in Optotrak global coordinate system (i = 1 to 12)
Singular value decomposition, e.g. Söderkvist and Wedin (1993), using divot coordinates measured in two coordinate systems can provide the following transformation matrix:
latex($T_{OC}$): transformation matrix from CAD based registration marker coordinate system to Optotrak global coordinate system
Using center of patella registration markers with this transformation matrix one can obtain:
latex($p_1^O$): center of the central/superior registration marker on the patella in Optotrak global coordinate system
latex($p_2^O$): center of the lateral registration marker on the patella in Optotrak global coordinate system
latex($p_3^O$): center of the medial registration marker on the patella in Optotrak global coordinate system
latex($T_{OP}$): transformation matrix from patella fixed registration marker coordinate system to Optotrak global coordinate system
The transformation matrix between patella and joint testing coordinate system can be obtained by following the steps outlined for the femur, see above.
Variables to establish the transformation matrix between patella and imaging coordinate systems are:
latex($p_1^I$): center of the central/superior registration marker on the patella in anatomical imaging coordinate system
latex($p_2^I$): center of the lateral registration marker on the patella in anatomical imaging coordinate system
latex($p_3^I$): center of the medial registration marker on the patella in anatomical imaging coordinate system
latex($o_P$): origin of the patella fixed registration marker coordinate system in anatomical imaging coordinate system
latex($u_P$): x-axis of the patella fixed registration marker coordinate system in anatomical imaging coordinate system
latex($v_P$): y-axis of the patella fixed registration marker coordinate system in anatomical imaging coordinate system
latex($w_P$): z-axis of the patella fixed registration marker coordinate system in anatomical imaging coordinate system
latex($T_{IP}$): transformation matrix from patella fixed registration marker coordinate system to anatomical imaging coordinate system
The transformation matrix between patella and imaging coordinate system can be obtained by following the steps outlined for the femur, see above.
References
Söderkvist I, Wedin PA. Determining the movements of the skeleton using well-configured markers. J Biomech. 1993 Dec;26(12):1473-7. [http://www.ncbi.nlm.nih.gov/pubmed/8308052 PubMed]