- Email: [email protected]
Using cine phase contrast magnetic resonance imaging to non-invasively study in vivo knee dynamics
Journal of Biomechanics 31 (1998) 21—26
Using cine phase contrast magnetic resonance imaging to non-invasively study in vivo knee dynamics Frances T. Sheehan!,",#, Felix E. Zajac!,#,$, John E. Drace",* ! Rehabilitation R&D Center, Veterans Affairs Palo Alto Health Care System, Palo Alto, CA 94304-1200, U.S.A. " Diagnostic Radiology Center, Veterans Affairs Palo Alto Health Care System, Palo Alto, CA 94304-1200, U.S.A. # Mechanical Engineering Department, Biomechanical Engineering Division, Stanford University, Stanford, CA 94305-4201, U.S.A. $ Department of Functional Restoration, Stanford University, Stanford, CA 94305-4201, U.S.A. Received in final form 9 October 1997
Abstract We tested the accuracy and feasibility of using cine phase contrast magnetic resonance imaging (cine-PC MRI) to non-invasively measure three-dimensional, in vivo, skeletal velocity. Bone displacement was estimated by integrating the velocity measurements. Cine-PC MRI was originally developed to directly and non-invasively measure in vivo blood and heart velocity. Since no standard of reference exists for in vivo measurement of trabecular bone motion, a motion phantom (consisting of a series of paired gears that moved a sample box containing a human femoral bone sample) was built to assess the accuracy of tracking trabecular bone with cine-PC MRI. The in-plane, average absolute displacement errors were 0.55$0.38 and 0.36$0.27 mm in the x- and y-direction, respectively. Thus, estimates of bone position based on the integration of bone velocity measurements are affected little by the magnetic properties of bone [Majumdar and Genant (1995) Osteoporos International 5, 79—92]. The velocity profiles of the patella, femur and tibia were measured in five healthy subjects during leg extensions. Extension was resisted by a 34 N weight. Subjects maintained a consistent motion rate (35$0.5 cycles min~1) and motion artifacts were minimal. Our results indicate that patellar flexion lags knee flexion and the patella tilts laterally and then medially as the knee extends. We conclude cine-PC MRI is a promising technique for the non-invasive measurement of in vivo skeletal dynamics and, based on our previous work, muscular dynamics as well. Published by Elsevier Science Ltd. Keywords: MRI; Femur; Tibia; Patella; Kinematics; Motion
1. Introduction Most kinematic and kinetic properties of the human musculoskeletal system cannot be measured directly, without the use of invasive techniques. For example, most techniques available to directly measure threedimensional bone motion are extremely invasive, e.g. bone screws and implantable markers (Lafortune et al., 1992; van Kampen and Huiskes, 1990), as are methods to measure tendon force (Fukashiro et al., 1995; Komi et al., 1987) and muscle/sarcomere motion (Lieber et al., 1994). Thus, muscle and bone kinematics and kinetics in humans are usually derived from musculoskeletal models and external measurements such as EMGs, external reaction forces, and the position of skin markers.
* Corresponding author. 0021-9290/98/$19.00 Published by Elsevier Science Ltd. PII S0021-9290(97)00109-7
Cine phase contrast (cine-PC) magnetic resonance imaging (MRI) (Pelc et al., 1991), a noninvasive technique, has been shown capable of measuring muscle fiber velocity, in vivo, during dynamic tasks (Drace and Pelc, 1994b). Through integration, ‘instantaneous’ measurements of tendon length (Drace and Pelc, 1994a) muscle fiber length, and moment arms can be derived. We now report the accuracy and feasibility of using cine-PC MRI to measure bone motion in vivo. Cine-PC MRI is the combination of two imaging techniques: cine MRI and phase-contrast MRI. In standard MRI, a static image is produced in which the contrast is based on the chemical environment of protons. Generally, a single acquisition takes seconds to minutes to collect, eliminating the possibility of imaging a rapidly moving object. Cine MRI compensates for periodic motion by collecting data continuously over many cycles and then retrospectively sorting the data using a
22
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
synchronization trigger. Thus, a series of quasi-static anatomic (magnitude) images portraying various phases of the motion cycle are collected during a single acquisition, lasting on the order of 128—256 cycles. The MRI signal is a complex quantity, having both magnitude and phase, which can be velocity-dependent. In phase-contrast MRI (PC MRI), velocity-dependent pulse sequences are used and velocity is extracted from the phase of the signal. PC MRI can thus quantify local velocity, independent of other MRI contrast mechanisms. Cine-PC MRI, by combining cine and phase-contrast techniques, provides one anatomic image and three (x, y and z) velocity images for each time frame (Fig. 1 B—E and Movie 1 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics). The three-dimensional position trajectory of any point, or region on the anatomic image, can be estimated by integrating the three velocity images. Since displacement is calculated through integration, its accuracy is independent of pixel size. Thus, accuracies can be well below one pixel. Velocity along the trajectory is unknown, a priori, but can be calculated along with the displacement trajectory. For example, the location of a point, selected in time frame 1, can be found in frame 2, since it displaces an amount (v *t) between frames. The velocity of this point, in the second frame, is now known and the process continues over the entire cycle (Pelc et al., 1995; Zhu et al., 1996). In order to achieve three-dimensional trajectories from a single imaging plane, the velocity at a point (x, y, z) is approximated by the velocity at point (x, y, z ), where z is the slice location. This approx0 0 imation is reasonable if either the out-of-plane motion is small, in comparison to image (slice) thickness, or the sample entering the imaging plane behaves similarly to the sample leaving.
2. Methods A motion phantom, consisting of a series of paired gears connected by plastic rods, was constructed (Fig. 1A). The rods, which held the top and bottom of a sample box, moved such that complex two-dimensional trajectories could be prescribed. The phantom’s plane of motion was aligned with the scanner’s x—y plane using the scanner’s alignment lights. The first sample box (SB1— CuSO ) contained CuSO -doped gelatin and the second 4 4 box (SB2—bone) consisted of a piece of human femoral bone with the bone marrow replaced with CuSO -doped 4 gelatin. A 2]4 grid of holes was milled through both boxes (and bone) so that each hole was 0.500A (12.700 mm) from its nearest neighbor. Plastic rods were inserted through the holes to create MRI signal voids (fiducials). Cine-PC images were taken in the x—y, y—z and x—z planes for both sample boxes with the use of a 1.5 T
Fig. 1. (A) Sketch of the motion phantom at time frame 3 (overall support structure not shown). An eight foot drive shaft connected the dc motor to the center gear through a secondary gearing system, allowing for variable motion rates. Gears, both in front (not shown) and in back, stabilized the sample box. (B) Magnitude image of SB1 — CuSO 4 phantom (time frame 3). Pixel size "0.9375 mm per pixel. Each image represents approximately 75 mm]75 mm. The fiducials are approximately 2.25 mm in diameter. (C) x-velocity image: For each pixel (full image"256]256 pixels) the value of the x-velocity is stored in an image file and can be displayed as a gray-scale image by using black, white, and varying gray levels to represent maximum positive, maximum negative, and submaximum velocities, respectively. For example, in the x-velocity image the top of the box is white, indicating a movement to the left (!x-direction), while the bottom is black, indicating a movement to the right (#x-direction). Thus, the box is rotating counterclockwise. (D) y-velocity image: the light-gray scale (negative velocity) indicates the box is moving downward (!y-direction). E) z-velocity image: the mid-gray level indicates zero z-velocity (i.e. planar movement). Note: Movie 1 (to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics) shows all 24 magnitude and velocity images in a cine movie loop.
imager (Signa; GE Medical Systems, Milwaukee, WI). The phantom moved at 30 cycles min~1, selected to closely mimic the knee joint study. The imaging parameters [TR (21 ms), TE (min full) and flip angle (30°)]
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
remained constant for all experiments. The temporal resolution, which is directly related to TR, was 84 ms, allowing the data to be divided into 24 frames. The MRI acquisitions were gated optically once per cycle. The imaging time varied from 4 min 12 s to 8 min 19 s. All experiments used a phased array of two 5 inch coils. The position trajectory of regions, approximately 7.5 mm]15 mm in size, in each sample were computed by integrating the velocity images (Drace and Pelc, 1994c). In addition, the movement of the box was quantified by manually tracking the centroid of each fiducial, using NIH Image, in all 24 magnitude images. The average absolute error over the entire cycle was calculated for each region by comparing the position trajectories derived by integrating the velocity images with those derived by manually tracking the fiducials. Five subjects were placed in a prone position and were asked to extend (under load) and flex their knee, from full extension to 40° degrees of flexion, at 35 cycles min~1, to the beat of a metronome (2 beats cycle~1). Cushions under the subjects freed the patella from external contact forces. An optical trigger marked the end of extension. The sagittal plane (Fig. 2 and Movie 2 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics) at the approximate centerline of the femur and patella was imaged in 7 min 30 s. Work is underway to reduce the imaging time while maintaining a high signal-to-noise ratio (SNR) [for a discussion of how imaging parameters affect scan time and SNR see McVeigh and Atalar (1993), Pelc et al. (1995), Riederer (1993)]. In addition, a cine acquisition (i.e., velocity was not measured) was used to collect anatomic images in four axial levels in 4 min 30 s. This study was approved by the Institutional Review Board (Medical Committee for the Protection of Human Subjects in Research) at Stanford University. Each subject signed a consent form prior to participation. At the end of each experiment, no subjects reported fatigue. By integrating the three-dimesional velocity images, regions selected on the femur, tibia, and patella, were tracked (Movie 2 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics). Each region contained the maximum area possible [i.e., the region had to remain within the bone and the available field of view (Fig. 2B)]. Patellar rotations were calculated using the displacement trajectories of the regions’ vertices (Kane et al., 1983). The local reference systems for the three bones (p"patella, f"femur, t"tibia) maintained the same general directionality as previous knee studies, where #x is medial (for the right leg), #y is superior, and #z is anterior when the leg is in ‘full extension’ (Hirokawa, 1991; Koh et al., 1992; van Kampen and Huiskes, 1990; Veress et al., 1979), but they were established by identifying anatomical landmarks on all three bones (Sheehan, 1997)
23
Fig. 2. Magnitude images for selected time frames during extension [(A): time frame 1; (B): time frame 6]. (A) The knee angle, g, was calculated as the angle between lines F1 and T1. F1 bisected the angle created by the anterior and posterior aspects of the femoral shaft (just superior to the femoral condyles). T1 was parallel to the anterior edge of the tibia (distal to the tibial head). (B) The two dashed lines represent the available field of view using two 5 inch coils. This frame shows the largest amount of artifacts, as compared to the images in the rest of the cycle, and even these artifacts are minimal. The use of a focused field of view improves image quality by reducing motion artifacts and improving the signal-to-noise ratio.
Fig. 3. Reference frames for the right femur (f , f , f ), patella (p , p , p ) x y z x y z and tibia (t , t , t ) derived from anatomical boney landmarks (see text). x y z Axial view is from the feet. The patellar and femoral anatomical landmarks were taken from the mid-patellar axial image and the axial image just superior to the posterior border of the sulcus groove, respectively. The two-dimensional angle between PL&P& and PP-P. is clinically defined as patellar tilt angle.
(Fig. 3): p "unit vector (PL&P&) f "unit vector (PP-P.) x x t "unit vector (PT#T"), z p "unit vector (p ]PP"P5), f "unit vector (f ]PF"F5), z x z x t "unit vector (PT-T"]t ), x z
24
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
p " unit vector (p ]p ), f "unit vector (f ]f ), y z x y z x t "unit vector (t ]t ), y z x where PA1A2 is the position vector from an arbitrary point A1 to another arbitrary point A2, Lf (Pf) the most lateral (posterior) point on the patella (Fig. 3B), Pt the most superior point of the patella (Fig. 3C), Pb the insertion of patellar tendon into the patella (Fig. 3C), Pl (Pm) the most posterior point on the lateral (medial) femoral condyle (Fig. 3B), PF2F1 the line along the anterior edge of the femur, proximal to the femoral condyles (Fig. 3C), PF3F4 the line along the posterior edge of the femur, proximal to the femoral condyles (Fig. 3C), PF"F5 the bisects the angle created by the lines PF1F2 and PF3F4 (Fig. 3C and line F1, Fig. 2), Tb the point on anterior edge of the tibia, imediately distal to the tibial plateau (Fig. 3C), Tc the most posterior point on the tibial plateau (Fig. 3C) and Tl the located along the anterior edge, distal to the tibial tuberosity (Fig. 3C).
3. Results The accuracy of manually tracking the fiducials using NIH Image was high. The average absolute error, comparing the interfiducial spacing on all 24 magnitude images to the actual interfiducial spacing (derived from the milling machine measurements) was 0.014 ($0.010) mm for both sample boxes. Thus, the position trajectory derived from the magnitude images estimates well the true position trajectory. This magnitude-image-based position trajectory can, therefore, be used to assess the accuracy of sample box position trajectories derived by integrating the cine-PC velocity images. The average absolute error (in-plane) over the entire cycle between the position trajectories, derived by integrating the velocity images and by manually tracking the fiducials was less than 0.7 mm for regions in the SB1CuSO and SB2-bone samples (Table 1). Tracking out4 of-plane motion (x—z and y—z plane studies) had slightly larger errors than tracking in-plane motion (x—y plane study). Since the regions moved &25 and &18 mm in
the x- and y-direction, respectively, the error was less than 3.5% (0.7/20 mm). We conclude that the errors are small enough to have confidence in the accuracy of cine-PC MRI velocity measurements. Our in vivo, three-dimensional patellar kinematics show, for most subjects, a lag in patellar extension (h ), 1 a lateral, then medial tilt (h ) and little change in patellar 2 rotation (h ) as the knee extends (Fig. 4). Plotting the 3 three-dimensional movement of the knee joint over time demonstrates these data well (Movies 3 and 4 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics). Each subject was able to maintain cyclic motion to within 0.5 cycles min~1 (1.4%) based on the recorded timing of the synchronization trigger. In comparison, one subject’s heart rate during a cine-PC MRI scan of the heart with the subject stationary varied from 54 to 72 bpm (33%). Due to this variability in heart rate, cine-PC MRI is designed to compensate for motion cycles that are not precisely the same length (Pelc et al., 1991). Finally, the average maximum out-ofplane patellar movement for all subjects was (4.00$ 1.50 mm) well under the image thickness (10 mm).
4. Discussion Our results indicate cine-PC MRI can accurately and non-invasively measure bone motion, in vivo, during dynamic tasks. Since the velocity measurements can be integrated to obtain position estimates, cine-PC MRI should be invaluable in estimating human muscle fiber and tendon architecture, and musculoskeletal geometry (e.g. moment arms) during motor tasks. However, since tendons provide insufficient MRI signal, tendon strain (Drace and Pelc, 1994a) can only be estimated by accurately tracking both bone (the insertion point) and muscle (the myotendinous junction) motion. The cine-PC imaging plane must be chosen carefully in order to minimize errors. Cine-PC MRI is presently limited, due to time restrictions, to a single slice per experiment. If the object being imaged has relatively small out-of-plane motion, as compared to the slice
Table 1 The average absolute tracking errors for the phantom study. The trajectory of each region was calculated both by tracking the centroid of each fiducial in all 24 magnitude images, using NIH image, and by integrating the velocity images from cine-PC MRI. The absolute difference in position from the two methods was averaged over all 24 time frames. Typically, two to nine regions, were analyzed for each study. In selecting the regions, care was taken not to enclose a fiducial within the region, since the lack of data would have caused larger errors Image plane
x—y (in-plane) y—z x—z
SB1—CuSO 4
SB2—bone
x(mm$SD)
y(mm$SD)
x(mm$SD)
y(mm$SD)
0.62$0.55 0.44$0.43 0.85$0.52
0.57$0.43 1.83$1.00 0.34$0.23
0.55$0.38 0.74$0.59 0.94$0.58
0.36$0.27 1.48$0.97 0.21$0.17
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
25
thickness (typically 10 mm), errors will be minimal (e.g. x—z plane, Table 1). Otherwise, larger errors may occur (e.g. y—z plane; Table 1). Since the out-of-plane patellar movement reported here is less than half the image thickness and the subject’s motion rate was consistent, we believe the accuracy of tracking the three-dimensional in vivo patellar-femoral kinematics is estimated well by the phantom study. Based on data from one subject who executed the extension task again without leaving the magnet, we believe the orientation angles (h , h and h ) 1 2 3 to be repeatable to within 2° (Sheehan, 1997). A more complete study is underway. h and h agree with data from the one subject re1 3 ported elsewhere (Koh et al., 1992), but h does not. 2 Other results, based on cadaver data, vary (Heegaard et al., 1994; Lafortune et al., 1992; van Kampen and Huiskes, 1990). A study by us is underway to evaluate the consistency of knee kinematics over a larger population. The noninvasive study of in vivo joint dynamics, both normal and pathologic, is a promising use of cine-PC MRI. This technique is based on the measurement of velocity, which can be integrated in order to track any point in the imaging plane. Thus, the accuracy is independent of pixel size and the need to manually track implanted markers (Heegaard et al., 1994; van Kampen and Huiskes, 1990), bone landmarks (Brossmann et al., 1993) or bone outlines (Crisco et al., 1995) is eliminated.
Acknowledgments This work was supported by NIH Grant HD31493, the Rehabilitation R&D Center and the Diagnostic Radiology Center of the Department of the Veterans Affairs (VA), and NIH Grant NS17662. We are grateful to Norbert Pelc, Thomas Kane and Paul Mitiguy for their help with this work and manuscript and to Jim Anderson and Doug Schwandt for their help in the design and building of experimental equipment.
References
Fig. 4. (A) h "patellar flexion, (B) h "tilt, and (C) h "twist (with 1 2 3 respect to the femur) during extension. Each symbol represents the same subject across all three plots. Note: the dashed line in A shows a 1 : 1 ratio of patellar flexion to knee flexion, in order to highlight the lag in patellar extension as the knee extends. The angles are calculated based on a xyz body-fixed rotation sequence. This rotation involves a P rotation of h , a P rotation of h , and a P rotation of h . x 1 y 2 z 3 A ‘P rotation of h ’ (of body P) implies a rotation of body P relative to x 1 body F during which a right-handed screw fixed in P with its axis parallel to P advances an amount h in the direction of P (Kane et al., x 1 x 1983).
Brossmann, J., Muhle, C., Schroder, C., Melchert, U., Bull, C., Spielmann, R., Heller, M., 1993. Patellar tracking patterns during active and passive knee extension: evaluation with motion-triggered cine MR imaging. Radiology 187, 205—212. Crisco, J., Hentel, K., Wolfe, S., Duncan, J., 1995. Two-dimensional rigid-body kinematics using image contour registration. Journal of Biomechanics 28, 119—124. Drace, J.E., Pelc, N.J., 1994a. Elastic deformation in tendons and myotendinous tissue: measurement by phase-contrast MR imaging. Radiology 191, 835—839. Drace, J.E., Pelc, N.J., 1994b. Measurement of skeletal muscle motion in vivo with phase-contrast MR imaging. Journal of Magnetic Resonante Imaging 4, 157—163.
26
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
Drace, J.E., Pelc, N.J., 1994c. Tracking the motion of skeletal muscle with velocity-encoded MR imagning. Journal of Magnetic Resonante Imaging 4, 773—778. Fukashiro, S., Komi, P., Jarvinen, M., Miyashita, M., 1995. In vivo Achilles tendon loading during jumping in humans. European Journal Applied Physiology 71, 453—458. Heegaard, J., Leyvraz, P., van Kampen, A., Rakotomanana, L., Rubin, P., Blankevoort, L., 1994. Influence of soft structures on patellar three-dimensional tracking. Clinical Orthopeadics 299, 235—243. Kane, T.R., Likins, P.W., Levinson, D.A., 1983. Spacecraft Dynamics. McGraw-Hill, New York. Koh, T., Grabiner, M., De Swart, R., 1992. In vivo tracking of the human patella. Journal of Biomechanics 25, 637—643. Komi, P., Salonen, M., Jarvinen, M., Kokko, O., 1987 March. In vivo registration of Achilles tendon forces in man. I. Methodological development. International Journal of Sports Medicine 8 (Suppl. 1), 3—8. Lafortune, M., Cavanagh, P., Sommer HJ, 3., Kalenak, A., 1992. Threedimensional kinematics of the human knee during walking. Journal of Biomechanics 25, 347—357. Lieber, R., Loren, G., Friden, J., 1994. In vivo measurement of human wrist extensor muscle sarcomere length changes. Journal of Neurophysiology 71, 874—881. McVeigh, E., Atalar, E., 1993. Balancing contrast, resolution, and signal-to-noise ratio in magnetic resonance imaging. In: Bronskill, M.J., Sprawls, P., (Eds.), The Physics of MRI 1992 AAPM Summer School Proceedings, American Institute of Physics, pp. 98—134.
Majumdar, S., Genant, H., 1995. A review of the recent advances in magnetic resonance imaging in the assessment of osteoporosis. Osteoporos International 5, 79—92. Pelc, N.J., Drangova, M., Pelc, L.R., Zhu, Y., Noll, D.C., Bowman, B.S., Herfkens, R.J., 1995. Tracking of cyclic motion with phase-contrast cine MR velocity data. Journal of Magnetic Resonance Imaging 5, 339—345. Pelc, N.J., Herfkens, R.J., Shimakawa, A., Enzmann, D.R., 1991. Phase contrast cine magnetic resonance imaging. Magnetic Resonance Q 7, 229—254. Riederer, S.J., 1993. Fast imaging techniques. In: Bronskill, M.J., Sprawls, P., (Eds.), The Physics of MRI 1992 AAPM Summer School Proceedings, American Institute of Physics, pp. 98—134. Sheehan, F.T., 1997. A noninvasive in-vivo study of the patella using cine phase contrast magnetic resonance imaging: three-dimensional kinematics and tendon strain. Doctoral thesis, Stanford University. van Kampen, A., Huiskes, R., 1990. The three-dimensional tracking pattern of the human patella. Journal of Orthopeadic Research 8, 372—382. Veress, S.A., Lippert, F.G., Hou, M.C., Takamoto, T., 1979. Patellar tracking patterns measurement by analytical X-ray photogrammetry. Journal of Biomechanics 12, 639—650. Zhu, Y., Drangova, M., Pelc, N.J., 1996. Fourier tracking of myocardial motion using cine-PC data. Magnetic Resonance Medicine 35, 471—480.
Using cine phase contrast magnetic resonance imaging to non-invasively study in vivo knee dynamics Frances T. Sheehan!,",#, Felix E. Zajac!,#,$, John E. Drace",* ! Rehabilitation R&D Center, Veterans Affairs Palo Alto Health Care System, Palo Alto, CA 94304-1200, U.S.A. " Diagnostic Radiology Center, Veterans Affairs Palo Alto Health Care System, Palo Alto, CA 94304-1200, U.S.A. # Mechanical Engineering Department, Biomechanical Engineering Division, Stanford University, Stanford, CA 94305-4201, U.S.A. $ Department of Functional Restoration, Stanford University, Stanford, CA 94305-4201, U.S.A. Received in final form 9 October 1997
Abstract We tested the accuracy and feasibility of using cine phase contrast magnetic resonance imaging (cine-PC MRI) to non-invasively measure three-dimensional, in vivo, skeletal velocity. Bone displacement was estimated by integrating the velocity measurements. Cine-PC MRI was originally developed to directly and non-invasively measure in vivo blood and heart velocity. Since no standard of reference exists for in vivo measurement of trabecular bone motion, a motion phantom (consisting of a series of paired gears that moved a sample box containing a human femoral bone sample) was built to assess the accuracy of tracking trabecular bone with cine-PC MRI. The in-plane, average absolute displacement errors were 0.55$0.38 and 0.36$0.27 mm in the x- and y-direction, respectively. Thus, estimates of bone position based on the integration of bone velocity measurements are affected little by the magnetic properties of bone [Majumdar and Genant (1995) Osteoporos International 5, 79—92]. The velocity profiles of the patella, femur and tibia were measured in five healthy subjects during leg extensions. Extension was resisted by a 34 N weight. Subjects maintained a consistent motion rate (35$0.5 cycles min~1) and motion artifacts were minimal. Our results indicate that patellar flexion lags knee flexion and the patella tilts laterally and then medially as the knee extends. We conclude cine-PC MRI is a promising technique for the non-invasive measurement of in vivo skeletal dynamics and, based on our previous work, muscular dynamics as well. Published by Elsevier Science Ltd. Keywords: MRI; Femur; Tibia; Patella; Kinematics; Motion
1. Introduction Most kinematic and kinetic properties of the human musculoskeletal system cannot be measured directly, without the use of invasive techniques. For example, most techniques available to directly measure threedimensional bone motion are extremely invasive, e.g. bone screws and implantable markers (Lafortune et al., 1992; van Kampen and Huiskes, 1990), as are methods to measure tendon force (Fukashiro et al., 1995; Komi et al., 1987) and muscle/sarcomere motion (Lieber et al., 1994). Thus, muscle and bone kinematics and kinetics in humans are usually derived from musculoskeletal models and external measurements such as EMGs, external reaction forces, and the position of skin markers.
* Corresponding author. 0021-9290/98/$19.00 Published by Elsevier Science Ltd. PII S0021-9290(97)00109-7
Cine phase contrast (cine-PC) magnetic resonance imaging (MRI) (Pelc et al., 1991), a noninvasive technique, has been shown capable of measuring muscle fiber velocity, in vivo, during dynamic tasks (Drace and Pelc, 1994b). Through integration, ‘instantaneous’ measurements of tendon length (Drace and Pelc, 1994a) muscle fiber length, and moment arms can be derived. We now report the accuracy and feasibility of using cine-PC MRI to measure bone motion in vivo. Cine-PC MRI is the combination of two imaging techniques: cine MRI and phase-contrast MRI. In standard MRI, a static image is produced in which the contrast is based on the chemical environment of protons. Generally, a single acquisition takes seconds to minutes to collect, eliminating the possibility of imaging a rapidly moving object. Cine MRI compensates for periodic motion by collecting data continuously over many cycles and then retrospectively sorting the data using a
22
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
synchronization trigger. Thus, a series of quasi-static anatomic (magnitude) images portraying various phases of the motion cycle are collected during a single acquisition, lasting on the order of 128—256 cycles. The MRI signal is a complex quantity, having both magnitude and phase, which can be velocity-dependent. In phase-contrast MRI (PC MRI), velocity-dependent pulse sequences are used and velocity is extracted from the phase of the signal. PC MRI can thus quantify local velocity, independent of other MRI contrast mechanisms. Cine-PC MRI, by combining cine and phase-contrast techniques, provides one anatomic image and three (x, y and z) velocity images for each time frame (Fig. 1 B—E and Movie 1 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics). The three-dimensional position trajectory of any point, or region on the anatomic image, can be estimated by integrating the three velocity images. Since displacement is calculated through integration, its accuracy is independent of pixel size. Thus, accuracies can be well below one pixel. Velocity along the trajectory is unknown, a priori, but can be calculated along with the displacement trajectory. For example, the location of a point, selected in time frame 1, can be found in frame 2, since it displaces an amount (v *t) between frames. The velocity of this point, in the second frame, is now known and the process continues over the entire cycle (Pelc et al., 1995; Zhu et al., 1996). In order to achieve three-dimensional trajectories from a single imaging plane, the velocity at a point (x, y, z) is approximated by the velocity at point (x, y, z ), where z is the slice location. This approx0 0 imation is reasonable if either the out-of-plane motion is small, in comparison to image (slice) thickness, or the sample entering the imaging plane behaves similarly to the sample leaving.
2. Methods A motion phantom, consisting of a series of paired gears connected by plastic rods, was constructed (Fig. 1A). The rods, which held the top and bottom of a sample box, moved such that complex two-dimensional trajectories could be prescribed. The phantom’s plane of motion was aligned with the scanner’s x—y plane using the scanner’s alignment lights. The first sample box (SB1— CuSO ) contained CuSO -doped gelatin and the second 4 4 box (SB2—bone) consisted of a piece of human femoral bone with the bone marrow replaced with CuSO -doped 4 gelatin. A 2]4 grid of holes was milled through both boxes (and bone) so that each hole was 0.500A (12.700 mm) from its nearest neighbor. Plastic rods were inserted through the holes to create MRI signal voids (fiducials). Cine-PC images were taken in the x—y, y—z and x—z planes for both sample boxes with the use of a 1.5 T
Fig. 1. (A) Sketch of the motion phantom at time frame 3 (overall support structure not shown). An eight foot drive shaft connected the dc motor to the center gear through a secondary gearing system, allowing for variable motion rates. Gears, both in front (not shown) and in back, stabilized the sample box. (B) Magnitude image of SB1 — CuSO 4 phantom (time frame 3). Pixel size "0.9375 mm per pixel. Each image represents approximately 75 mm]75 mm. The fiducials are approximately 2.25 mm in diameter. (C) x-velocity image: For each pixel (full image"256]256 pixels) the value of the x-velocity is stored in an image file and can be displayed as a gray-scale image by using black, white, and varying gray levels to represent maximum positive, maximum negative, and submaximum velocities, respectively. For example, in the x-velocity image the top of the box is white, indicating a movement to the left (!x-direction), while the bottom is black, indicating a movement to the right (#x-direction). Thus, the box is rotating counterclockwise. (D) y-velocity image: the light-gray scale (negative velocity) indicates the box is moving downward (!y-direction). E) z-velocity image: the mid-gray level indicates zero z-velocity (i.e. planar movement). Note: Movie 1 (to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics) shows all 24 magnitude and velocity images in a cine movie loop.
imager (Signa; GE Medical Systems, Milwaukee, WI). The phantom moved at 30 cycles min~1, selected to closely mimic the knee joint study. The imaging parameters [TR (21 ms), TE (min full) and flip angle (30°)]
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
remained constant for all experiments. The temporal resolution, which is directly related to TR, was 84 ms, allowing the data to be divided into 24 frames. The MRI acquisitions were gated optically once per cycle. The imaging time varied from 4 min 12 s to 8 min 19 s. All experiments used a phased array of two 5 inch coils. The position trajectory of regions, approximately 7.5 mm]15 mm in size, in each sample were computed by integrating the velocity images (Drace and Pelc, 1994c). In addition, the movement of the box was quantified by manually tracking the centroid of each fiducial, using NIH Image, in all 24 magnitude images. The average absolute error over the entire cycle was calculated for each region by comparing the position trajectories derived by integrating the velocity images with those derived by manually tracking the fiducials. Five subjects were placed in a prone position and were asked to extend (under load) and flex their knee, from full extension to 40° degrees of flexion, at 35 cycles min~1, to the beat of a metronome (2 beats cycle~1). Cushions under the subjects freed the patella from external contact forces. An optical trigger marked the end of extension. The sagittal plane (Fig. 2 and Movie 2 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics) at the approximate centerline of the femur and patella was imaged in 7 min 30 s. Work is underway to reduce the imaging time while maintaining a high signal-to-noise ratio (SNR) [for a discussion of how imaging parameters affect scan time and SNR see McVeigh and Atalar (1993), Pelc et al. (1995), Riederer (1993)]. In addition, a cine acquisition (i.e., velocity was not measured) was used to collect anatomic images in four axial levels in 4 min 30 s. This study was approved by the Institutional Review Board (Medical Committee for the Protection of Human Subjects in Research) at Stanford University. Each subject signed a consent form prior to participation. At the end of each experiment, no subjects reported fatigue. By integrating the three-dimesional velocity images, regions selected on the femur, tibia, and patella, were tracked (Movie 2 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics). Each region contained the maximum area possible [i.e., the region had to remain within the bone and the available field of view (Fig. 2B)]. Patellar rotations were calculated using the displacement trajectories of the regions’ vertices (Kane et al., 1983). The local reference systems for the three bones (p"patella, f"femur, t"tibia) maintained the same general directionality as previous knee studies, where #x is medial (for the right leg), #y is superior, and #z is anterior when the leg is in ‘full extension’ (Hirokawa, 1991; Koh et al., 1992; van Kampen and Huiskes, 1990; Veress et al., 1979), but they were established by identifying anatomical landmarks on all three bones (Sheehan, 1997)
23
Fig. 2. Magnitude images for selected time frames during extension [(A): time frame 1; (B): time frame 6]. (A) The knee angle, g, was calculated as the angle between lines F1 and T1. F1 bisected the angle created by the anterior and posterior aspects of the femoral shaft (just superior to the femoral condyles). T1 was parallel to the anterior edge of the tibia (distal to the tibial head). (B) The two dashed lines represent the available field of view using two 5 inch coils. This frame shows the largest amount of artifacts, as compared to the images in the rest of the cycle, and even these artifacts are minimal. The use of a focused field of view improves image quality by reducing motion artifacts and improving the signal-to-noise ratio.
Fig. 3. Reference frames for the right femur (f , f , f ), patella (p , p , p ) x y z x y z and tibia (t , t , t ) derived from anatomical boney landmarks (see text). x y z Axial view is from the feet. The patellar and femoral anatomical landmarks were taken from the mid-patellar axial image and the axial image just superior to the posterior border of the sulcus groove, respectively. The two-dimensional angle between PL&P& and PP-P. is clinically defined as patellar tilt angle.
(Fig. 3): p "unit vector (PL&P&) f "unit vector (PP-P.) x x t "unit vector (PT#T"), z p "unit vector (p ]PP"P5), f "unit vector (f ]PF"F5), z x z x t "unit vector (PT-T"]t ), x z
24
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
p " unit vector (p ]p ), f "unit vector (f ]f ), y z x y z x t "unit vector (t ]t ), y z x where PA1A2 is the position vector from an arbitrary point A1 to another arbitrary point A2, Lf (Pf) the most lateral (posterior) point on the patella (Fig. 3B), Pt the most superior point of the patella (Fig. 3C), Pb the insertion of patellar tendon into the patella (Fig. 3C), Pl (Pm) the most posterior point on the lateral (medial) femoral condyle (Fig. 3B), PF2F1 the line along the anterior edge of the femur, proximal to the femoral condyles (Fig. 3C), PF3F4 the line along the posterior edge of the femur, proximal to the femoral condyles (Fig. 3C), PF"F5 the bisects the angle created by the lines PF1F2 and PF3F4 (Fig. 3C and line F1, Fig. 2), Tb the point on anterior edge of the tibia, imediately distal to the tibial plateau (Fig. 3C), Tc the most posterior point on the tibial plateau (Fig. 3C) and Tl the located along the anterior edge, distal to the tibial tuberosity (Fig. 3C).
3. Results The accuracy of manually tracking the fiducials using NIH Image was high. The average absolute error, comparing the interfiducial spacing on all 24 magnitude images to the actual interfiducial spacing (derived from the milling machine measurements) was 0.014 ($0.010) mm for both sample boxes. Thus, the position trajectory derived from the magnitude images estimates well the true position trajectory. This magnitude-image-based position trajectory can, therefore, be used to assess the accuracy of sample box position trajectories derived by integrating the cine-PC velocity images. The average absolute error (in-plane) over the entire cycle between the position trajectories, derived by integrating the velocity images and by manually tracking the fiducials was less than 0.7 mm for regions in the SB1CuSO and SB2-bone samples (Table 1). Tracking out4 of-plane motion (x—z and y—z plane studies) had slightly larger errors than tracking in-plane motion (x—y plane study). Since the regions moved &25 and &18 mm in
the x- and y-direction, respectively, the error was less than 3.5% (0.7/20 mm). We conclude that the errors are small enough to have confidence in the accuracy of cine-PC MRI velocity measurements. Our in vivo, three-dimensional patellar kinematics show, for most subjects, a lag in patellar extension (h ), 1 a lateral, then medial tilt (h ) and little change in patellar 2 rotation (h ) as the knee extends (Fig. 4). Plotting the 3 three-dimensional movement of the knee joint over time demonstrates these data well (Movies 3 and 4 — to be included in the forthcoming supplementary CD-ROM to the Journal of Biomechanics). Each subject was able to maintain cyclic motion to within 0.5 cycles min~1 (1.4%) based on the recorded timing of the synchronization trigger. In comparison, one subject’s heart rate during a cine-PC MRI scan of the heart with the subject stationary varied from 54 to 72 bpm (33%). Due to this variability in heart rate, cine-PC MRI is designed to compensate for motion cycles that are not precisely the same length (Pelc et al., 1991). Finally, the average maximum out-ofplane patellar movement for all subjects was (4.00$ 1.50 mm) well under the image thickness (10 mm).
4. Discussion Our results indicate cine-PC MRI can accurately and non-invasively measure bone motion, in vivo, during dynamic tasks. Since the velocity measurements can be integrated to obtain position estimates, cine-PC MRI should be invaluable in estimating human muscle fiber and tendon architecture, and musculoskeletal geometry (e.g. moment arms) during motor tasks. However, since tendons provide insufficient MRI signal, tendon strain (Drace and Pelc, 1994a) can only be estimated by accurately tracking both bone (the insertion point) and muscle (the myotendinous junction) motion. The cine-PC imaging plane must be chosen carefully in order to minimize errors. Cine-PC MRI is presently limited, due to time restrictions, to a single slice per experiment. If the object being imaged has relatively small out-of-plane motion, as compared to the slice
Table 1 The average absolute tracking errors for the phantom study. The trajectory of each region was calculated both by tracking the centroid of each fiducial in all 24 magnitude images, using NIH image, and by integrating the velocity images from cine-PC MRI. The absolute difference in position from the two methods was averaged over all 24 time frames. Typically, two to nine regions, were analyzed for each study. In selecting the regions, care was taken not to enclose a fiducial within the region, since the lack of data would have caused larger errors Image plane
x—y (in-plane) y—z x—z
SB1—CuSO 4
SB2—bone
x(mm$SD)
y(mm$SD)
x(mm$SD)
y(mm$SD)
0.62$0.55 0.44$0.43 0.85$0.52
0.57$0.43 1.83$1.00 0.34$0.23
0.55$0.38 0.74$0.59 0.94$0.58
0.36$0.27 1.48$0.97 0.21$0.17
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
25
thickness (typically 10 mm), errors will be minimal (e.g. x—z plane, Table 1). Otherwise, larger errors may occur (e.g. y—z plane; Table 1). Since the out-of-plane patellar movement reported here is less than half the image thickness and the subject’s motion rate was consistent, we believe the accuracy of tracking the three-dimensional in vivo patellar-femoral kinematics is estimated well by the phantom study. Based on data from one subject who executed the extension task again without leaving the magnet, we believe the orientation angles (h , h and h ) 1 2 3 to be repeatable to within 2° (Sheehan, 1997). A more complete study is underway. h and h agree with data from the one subject re1 3 ported elsewhere (Koh et al., 1992), but h does not. 2 Other results, based on cadaver data, vary (Heegaard et al., 1994; Lafortune et al., 1992; van Kampen and Huiskes, 1990). A study by us is underway to evaluate the consistency of knee kinematics over a larger population. The noninvasive study of in vivo joint dynamics, both normal and pathologic, is a promising use of cine-PC MRI. This technique is based on the measurement of velocity, which can be integrated in order to track any point in the imaging plane. Thus, the accuracy is independent of pixel size and the need to manually track implanted markers (Heegaard et al., 1994; van Kampen and Huiskes, 1990), bone landmarks (Brossmann et al., 1993) or bone outlines (Crisco et al., 1995) is eliminated.
Acknowledgments This work was supported by NIH Grant HD31493, the Rehabilitation R&D Center and the Diagnostic Radiology Center of the Department of the Veterans Affairs (VA), and NIH Grant NS17662. We are grateful to Norbert Pelc, Thomas Kane and Paul Mitiguy for their help with this work and manuscript and to Jim Anderson and Doug Schwandt for their help in the design and building of experimental equipment.
References
Fig. 4. (A) h "patellar flexion, (B) h "tilt, and (C) h "twist (with 1 2 3 respect to the femur) during extension. Each symbol represents the same subject across all three plots. Note: the dashed line in A shows a 1 : 1 ratio of patellar flexion to knee flexion, in order to highlight the lag in patellar extension as the knee extends. The angles are calculated based on a xyz body-fixed rotation sequence. This rotation involves a P rotation of h , a P rotation of h , and a P rotation of h . x 1 y 2 z 3 A ‘P rotation of h ’ (of body P) implies a rotation of body P relative to x 1 body F during which a right-handed screw fixed in P with its axis parallel to P advances an amount h in the direction of P (Kane et al., x 1 x 1983).
Brossmann, J., Muhle, C., Schroder, C., Melchert, U., Bull, C., Spielmann, R., Heller, M., 1993. Patellar tracking patterns during active and passive knee extension: evaluation with motion-triggered cine MR imaging. Radiology 187, 205—212. Crisco, J., Hentel, K., Wolfe, S., Duncan, J., 1995. Two-dimensional rigid-body kinematics using image contour registration. Journal of Biomechanics 28, 119—124. Drace, J.E., Pelc, N.J., 1994a. Elastic deformation in tendons and myotendinous tissue: measurement by phase-contrast MR imaging. Radiology 191, 835—839. Drace, J.E., Pelc, N.J., 1994b. Measurement of skeletal muscle motion in vivo with phase-contrast MR imaging. Journal of Magnetic Resonante Imaging 4, 157—163.
26
F.T. Sheehan et al. / Journal of Biomechanics 31 (1998) 21—26
Drace, J.E., Pelc, N.J., 1994c. Tracking the motion of skeletal muscle with velocity-encoded MR imagning. Journal of Magnetic Resonante Imaging 4, 773—778. Fukashiro, S., Komi, P., Jarvinen, M., Miyashita, M., 1995. In vivo Achilles tendon loading during jumping in humans. European Journal Applied Physiology 71, 453—458. Heegaard, J., Leyvraz, P., van Kampen, A., Rakotomanana, L., Rubin, P., Blankevoort, L., 1994. Influence of soft structures on patellar three-dimensional tracking. Clinical Orthopeadics 299, 235—243. Kane, T.R., Likins, P.W., Levinson, D.A., 1983. Spacecraft Dynamics. McGraw-Hill, New York. Koh, T., Grabiner, M., De Swart, R., 1992. In vivo tracking of the human patella. Journal of Biomechanics 25, 637—643. Komi, P., Salonen, M., Jarvinen, M., Kokko, O., 1987 March. In vivo registration of Achilles tendon forces in man. I. Methodological development. International Journal of Sports Medicine 8 (Suppl. 1), 3—8. Lafortune, M., Cavanagh, P., Sommer HJ, 3., Kalenak, A., 1992. Threedimensional kinematics of the human knee during walking. Journal of Biomechanics 25, 347—357. Lieber, R., Loren, G., Friden, J., 1994. In vivo measurement of human wrist extensor muscle sarcomere length changes. Journal of Neurophysiology 71, 874—881. McVeigh, E., Atalar, E., 1993. Balancing contrast, resolution, and signal-to-noise ratio in magnetic resonance imaging. In: Bronskill, M.J., Sprawls, P., (Eds.), The Physics of MRI 1992 AAPM Summer School Proceedings, American Institute of Physics, pp. 98—134.
Majumdar, S., Genant, H., 1995. A review of the recent advances in magnetic resonance imaging in the assessment of osteoporosis. Osteoporos International 5, 79—92. Pelc, N.J., Drangova, M., Pelc, L.R., Zhu, Y., Noll, D.C., Bowman, B.S., Herfkens, R.J., 1995. Tracking of cyclic motion with phase-contrast cine MR velocity data. Journal of Magnetic Resonance Imaging 5, 339—345. Pelc, N.J., Herfkens, R.J., Shimakawa, A., Enzmann, D.R., 1991. Phase contrast cine magnetic resonance imaging. Magnetic Resonance Q 7, 229—254. Riederer, S.J., 1993. Fast imaging techniques. In: Bronskill, M.J., Sprawls, P., (Eds.), The Physics of MRI 1992 AAPM Summer School Proceedings, American Institute of Physics, pp. 98—134. Sheehan, F.T., 1997. A noninvasive in-vivo study of the patella using cine phase contrast magnetic resonance imaging: three-dimensional kinematics and tendon strain. Doctoral thesis, Stanford University. van Kampen, A., Huiskes, R., 1990. The three-dimensional tracking pattern of the human patella. Journal of Orthopeadic Research 8, 372—382. Veress, S.A., Lippert, F.G., Hou, M.C., Takamoto, T., 1979. Patellar tracking patterns measurement by analytical X-ray photogrammetry. Journal of Biomechanics 12, 639—650. Zhu, Y., Drangova, M., Pelc, N.J., 1996. Fourier tracking of myocardial motion using cine-PC data. Magnetic Resonance Medicine 35, 471—480.