A Method for Measurement of Joint Kinematics in Vivo by Registration of 3-D Geometric Models With Cine Phase Contrast Magnetic Resonance Imaging Data

[+] Author and Article Information
Peter J. Barrance, Glenn N. Williams, John E. Novotny

Center for Biomedical Engineering Research,  Department of Mechanical Engineering, 126 Spencer Laboratories, University of Delaware, Newark, DE 19716

Thomas S. Buchanan1

Center for Biomedical Engineering Research,  Department of Mechanical Engineering, 126 Spencer Laboratories, University of Delaware, Newark, DE 19716

The transformation specifies the pose of the second coordinate system, denoted by the left subscript, relative to the first coordinate system, denoted by the left superscript.


Corresponding author; e-mail: buchanan@me.udel.edu

J Biomech Eng 127(5), 829-837 (May 31, 2005) (9 pages) doi:10.1115/1.1992524 History: Received March 28, 2004; Revised May 19, 2005; Accepted May 31, 2005

A new method is presented for measuring joint kinematics by optimally matching modeled trajectories of geometric surface models of bones with cine phase contrast (cine-PC) magnetic resonance imaging data. The incorporation of the geometric bone models (GBMs) allows computation of kinematics based on coordinate systems placed relative to full 3-D anatomy, as well as quantification of changes in articular contact locations and relative velocities during dynamic motion. These capabilities are additional to those of cine-PC based techniques that have been used previously to measure joint kinematics during activity. Cine-PC magnitude and velocity data are collected on a fixed image plane prescribed through a repetitively moved skeletal joint. The intersection of each GBM with a simulated image plane is calculated as the model moves along a computed trajectory, and cine-PC velocity data are sampled from the regions of the velocity images within the area of this intersection. From the sampled velocity data, the instantaneous linear and angular velocities of a coordinate system fixed to the GBM are estimated, and integration of the linear and angular velocities is used to predict updated trajectories. A moving validation phantom that produces motions and velocity data similar to those observed in an experiment on human knee kinematics was designed. This phantom was used to assess cine-PC rigid body tracking performance by comparing the kinematics of the phantom measured by this method to similar measurements made using a magnetic tracking system. Average differences between the two methods were measured as 2.82 mm rms for anterior∕posterior tibial position, and 2.63 deg rms for axial rotation. An inter-trial repeatability study of human knee kinematics using the new method produced rms differences in anterior∕posterior tibial position and axial rotation of 1.44 mm and 2.35 deg. The performance of the method is concluded to be sufficient for the effective study of kinematic changes caused to knees by soft tissue injuries.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Subject positioning and equipment for the in vivo study: (a) knee positioning jig, (b) magnetic resonance signal receiving coils, (c) optical trigger, (d) magnetic resonance scanner

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Figure 2

Cine phase contrast (cine-PC) acquisition plane and data. (a) The image plane coordinate system P is located relative to the global coordinate system G. (b) At each time frame, the cine-PC magnitude image provides a sectional view through the anatomy. (c),(d),(e) Three components of the measured velocity vectors at each pixel are encoded in grayscale images. The darker shaded arrows in the velocity images indicate the direction of the velocity component encoded in that image. The gray scale below the images indicates the magnitudes and signs of the velocity components.

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Figure 3

Graphical bone models (GBMs) and anatomical coordinate systems for the knee extension experiment. (a) The inferior∕superior axis of the femur was aligned by bisecting landmarks in a static sagittal plane image of the knee. (b),(c) The medial∕lateral axis of the femur was aligned parallel to planes tangent to the most posterior and inferior surfaces of each condyle. The femoral landmark for measuring joint position parameters was at the most distal point in the femoral notch. (d) The inferior∕superior axis of the tibia was aligned with a similar method to that of the femur. (e),(f) The tibia’s medial∕lateral axis was oriented parallel to planes tangent to the most posterior surfaces of the tibia∕fibula and the tibial plateau. The tibial landmark for measuring joint position parameters was the midpoint of the tibial intercondylar eminences. For both femur and tibia, the inclinations of the alignment planes in the sagittal view were determined by the inferior∕superior axis directions as described above.

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Figure 4

Geometric bone model kinematics (GBM), cross-sectional image generation, and velocity data extraction. (a) Coordinate system L is fixed in the GBM. At the reference position of the GBM, coordinate systems L and P coincide. (b) Changes in position during motion are modeled by the relationship of L relative to P. (c),(d) A simulated bone intersection image is created based on the modeled position. (e) Velocity data are sampled from the pixels of the cine-PC images corresponding to the interior region of the modeled bone intersection for trajectory prediction. The correspondence between the simulated intersection and the observed bone outline in the cine-PC magnitude image is used for pose optimization.

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Figure 5

Schematic of the interaction between the pose optimization and trajectory prediction processes. The initial 3-D pose of the bone is adjusted to minimize a penalty function that evaluates the overall correspondence of the simulated bone intersection with the bone position seen in the magnitude images over the entire computed trajectory (pose optimization). Individual trajectories are calculated by optimizing the trajectory derivatives for each data frame according to the error between modeled and observed velocity data fields on the predicted region of intersection of the bone in the image (trajectory prediction).

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Figure 6

Motion phantom for the validation experiment. (a,b) enclosures for femur, tibia specimens, (c) bevel gear linkage creating 1:4 axial rotation of tibial enclosure with flexion, (d) control rod connected to servomotor, (e) block to cover MR scanner’s optical trigger, (f) multimodality imaging marker, (g) counterweight to balance tibia enclosure, (h) magnetic tracking sensor, (i) magnetic tracking transmitter, (j) knee jig used in human experiment.

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Figure 7

Geometric models of bovine bone specimens used in motion phantom. (a) Distal femur, showing femoral landmark LMfem. (b) Proximal tibia, showing tibial landmarks LM1 through LM5.

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Figure 8

Axial rotation vs flexion angle measured by magnetic tracking and cine-PC tracking methods for the in vitro validation experiment. Several cycles of data are shown for the magnetic tracking method; one representative cycle was used in the analysis. The extension (upward traveling) phase of the phantom’s motion is indicated by the asterisks on each curve.

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Figure 9

Anterior position parameters as measured by the magnetic tracking and cine-PC tracking method for the in vitro validation experiment. (a) Landmarks LM1, LM4. (b) Landmarks LM2, LM3, LM5.

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Figure 10

Results of repeated measurements (Trial 1, Trial 2) of in vivo tibiofemoral kinematics for one subject. (a) Tibial anterior∕posterior position vs flexion angle. (b) Tibial axial rotation angle vs. flexion angle. The stars on the curves identify the portion of each loop that corresponds to the phase in which the knees were being extended.




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