Technical Note

Design and Validation of a Motion Stage for In VitroMR Experiments

Yong Zhou, PhD,* Timothy J. Carroll, PhD, Thomas M. Grist, MD, and Richard Frayne, PhD

A computer-controlled motion stage was designed to facili-tate motion studies and simulations of cardiac magneticresonance (MR) experiments. The stage was constructed tomove a phantom of up to 6 kg at velocities up to 15 cm/secalong a two-dimensional trajectory within an MR scanner.The operation of the motion stage was validated and foundto be accurate to within 0.08 cm in displacement and 1.5cm/sec in velocity (root-mean-square error). No imagedegradation was observed. J. Magn. Reson. Imaging 1999;10:972–977. r 1999 Wiley-Liss, Inc.

Index terms: motion stage; motion studies; cardiac imagingsimulations

INTRODUCTION

MOTION-RELATED phenomena are of great interest inMR. In particular, the study and correction of motionartifacts (1,2), as well as the characterizations of cardiacmotion (3–5) and cardiac flow rates (4,6,7), are activeareas of research. It is frequently advantageous to studythese phenomena using an in vitro system (2,3,5–7).Here we present the design and validation of an inexpen-sive and easy-to-use motion stage that is ideally suitedfor these experiments. The design goals of this motionstage were that it should be able to translate a phantomaccurately and precisely (#6 kg) at a velocity of up to 15cm/sec along a trajectory in the horizontal plane withinthe MR scanner bore. Simultaneous motion in both thephase- and frequency-encoding directions were essen-tial. These design goals were selected to allow modelsimulations of cardiac motion during MR measurementof coronary flow (4,6,7).

MATERIALS AND METHODS

Motion Stage Design

The motion stage consisted of three components: astepping motor and drive train, a drive shaft, and aplatform assembly (Fig. 1a). Plastic, delrin, and plywoodwere used in constructing the platform assembly thatoperated within the scanner bore, because these materi-als do not induce susceptibility artifacts in the image.Portions of the drive train, however, were made fromaluminum, steel, and stainless steel. These parts wereat least 250 cm from the isocenter of the magnet, so thatthey had no adverse effect on the image quality. Theentire assembly was mounted on four interconnecting92 cm long sections of plywood. The plywood baserested on the patient couch and extended into the boreof the magnet, where the platform assembly was posi-tioned at the magnet isocenter.

The stepping motor (PDX13-83-62P; Parker, RohnertPark, CA) that drove the motion stage was located 280cm from the magnet isocenter. No magnetic shieldingwas placed around the motor; however, the motor wasenclosed in an aluminum box. The motor-control cableswere shielded by a metal-mesh sock and entered thescanner room via a wave-guide. This metal-mesh sockwas attached to the aluminum box at one end andgrounded to the wave-guide at the other end. Shieldingand grounding the motor were effective in minimizingnoise in the MR image.

The motor was powered by a motor indexer that wascontrolled by a personal computer (Macintosh Quadra800; Apple Computer, Cupertino, CA) running LAB-VIEW software (National Instruments, Austin, TX)through an RS-232 serial port. A simple motion controlscheme was implemented using LABVIEW software togenerate arbitrary motion waveforms as well as a triggersignal that could mimic an electrocardiogram (ECG)signal for cardiac gating.

Two aluminum L-shaped brackets were used to sup-port both the motor and the axle (Fig. 1b). The motorwas mounted on one of the brackets and drove a gearsystem that was mounted on the axle supported by bothbrackets. The axle that supported the pinion gear wasmounted in two stainless steel ball bearings that werepressed fit into both brackets. The rack was mounted ontop of a stainless steel linear rail guide (ThompsonIndustries, Linear Motion Systems, Port Washington,

Departments of Medical Physics and Radiology, University of Wisconsin—Madison, E3/311 Clinical Science Center, 600 Highland Avenue, Madi-son, Wisconsin 53792-3252.Contract grant sponsor: National Institutes of Health; Contract grantnumbers: R01 HL52747 and R29 HL57501; Contract grant sponsor:Whitaker Foundation; Contract grant number: RG-96-0485.Submitted for presentation at the ISMRM Annual Meeting, Philadel-phia, 1999.Richard Frayne’s current address is Seaman Family MR Center, Foot-hills Medical Center/University of Calgary, 1403 29th Street NW,Calgary AB Canada T2N 2T9.*Address reprint requests to: Y.Z., GE Medical Systems, P.O. Box 414,W832, Milwaukee, WI 53201. E-mail: yong.zhou@med.ge.comReceived March 9, 1999; Accepted June 15, 1999.

JOURNAL OF MAGNETIC RESONANCE IMAGING 10:972–977 (1999)

r 1999 Wiley-Liss, Inc. 972

NY). An outrigger was used to eliminate rotation aboutthe longitudinal axis of the drive shaft.

The platform assembly consisted of a supporting rail,a movable cart that was free to move in the longitudinaldirection (ie, parallel to the shaft axis), a movablemounting block that was free to move in the transversedirection (ie, perpendicular to the shaft axis), a slottedplate, and a phantom (Fig. 1c). The phantom wasmounted on the mounting block using two pins thatpassed through the slotted plate (Fig. 1d). Since themounting block was free to move both parallel andperpendicular to the drive shaft, the phantom wouldfollow the trajectory defined by the slots in the plate. Awide range of motions along both the longitudinal andtransverse directions was possible by using differentslot geometries. A plate with slots at 45° to the driveshaft axis was used during these experiments.

Validation

Two important aspects of the evaluation of a motionstage that operates inside a MR scanner are a) to ensurethat the device does not degrade image quality (ie,decrease signal-to-noise ratio [SNR] or induce imageartifact); and b) to estimate the accuracy, precision, andreliability during operation.

Image Quality Comparison

A series of images of a static agar phantom wereacquired under two different configurations using atwo-dimensional (2D) gradient-recalled-echo (GRE) im-aging sequence (tip angle/TR/TE 20°/50 msec/10 msec,field of view (FOV) 32 cm 3 32 cm, slice thickness 1 cm,

acquisition matrix 256 3 256). The bandwidth usedhere matched that used in motion studies later. The twoconfigurations were as follows: (A) only the platformassembly was in the magnet bore, ie, the motor andcables were not in the scanner room; (B) the motionstage was fully assembled and running, but the phan-tom assembly was disengaged from the drive shaft. Thesame phantom was used in both configurations, andcare was taken to ensure that the phantom remained atthe same position during imaging. The images wereanalyzed by placing regions of interest (ROI) in a uni-form area of the phantom and in air. The average of theROI values in the air was multiplied by Ï2/p and takenas the noise value (8). The SNR was obtained by dividingthe phantom ROI value by the noise value.

Calibration

To access the accuracy, precision, and reliability of themotion stage, a series of tests were performed bothoutside and within a 1.5 T clinical MR scanner (Signa;General Electric Medical Systems, Waukesha, WI). First,the calibration constant (K), which relates the lineardisplacement of the phantom and the prescribed motion(in revolutions), was obtained. To obtain K, the motionstage was programmed to move a specified number ofrevolutions (R), and the net displacement (D) was mea-sured using a ruler attached to the guide rail. Toeliminate the effect of mechanical backlash duringcalibration, the motion stage was always moved to thestarting position and then was moved along the samedirection to the ending position. The starting positionand the ending position were recorded, and the net

Figure 1. Schematic diagram of the motion stage (not to scale). a: Side view of the complete motion stage. b: Top view of the drivetrain. c: Top view of the platform assembly without the slotted plate. d: Slotted plate used in this study.

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displacement was calculated. This measurement wasrepeated 33 times for a range of revolutions from 0.15 to6.25 rev; 26 measurements were performed outside ofthe scanner, and 7 measurements were done inside thescanner. Different motion profiles were used to test thedependence of K on velocity and acceleration. Linearregression (D 5 K · R) was used to determine K.

Motion Profile Validation

Two independent methods were used to test the accu-racy and reproducibility of the motion profiles. In thefirst method, an ultrasonic motion sensor (PASCO CI-6521A; Roseville, CA) was used to monitor the positionof the phantom at 50 msec intervals outside the scannerroom. The accuracy and precision of this sensor are 0.2and 0.1 cm, respectively.

In the second method, MR images were acquired andanalyzed to obtain the position and velocity of themoving phantom at different times during a motioncycle. First, a cardiac-gated 2D GRE imaging sequence(tip angle/TR/TE 30°/12 msec/4 msec) with prospec-tive triggering was used to acquire images to estimatethe phantom displacement. The FOV was 32 3 32 cm sothat the entire range of motion was covered. The acqui-sition slab was oriented in the horizontal plane, inwhich the phantom was moving, so that both thelongitudinal and perpendicular displacements could besimultaneously measured from each image. The slicethickness was 1 cm, and the acquisition matrix was 512 3512 with 2 signal averages. As the simulated ECG signalrate was 33 bpm, 120 phases were acquired over 31minutes and 9 seconds. The phantom position wasdetermined by finding the edge position of the phantomin each image. The error in these position values wasestimated to be 60.03 cm (half of the pixel size). Timinguncertainty of the MR scanner was estimated to be lessthan 1 msec. A cine phase contrast (PC) sequence wasused to measure the velocity of the phantom. The dataacquisition parameters were as follows: tip angle/

TE/TR 30°/7.6 msec/17 msec, FOV 32 cm 3 32 cm,slice thickness 1 cm, acquisition matrix 256 3 256.Velocity in the longitudinal direction was encoded usinga velocity encoding of 30 cm/sec. ROIs were placed onthe phase difference images. The average value and thestandard deviation of the ROIs provided estimates of thevelocity and the precision in the velocity, respectively.Total scan time was 7 minutes 34 seconds, and 32phases were reconstructed.

Two waveforms with different velocity profiles wereevaluated using the above methods. The first waveformconsisted of a single trapezoid and the second consistedof a superposition of trapezoids. The parameters forthese waveforms are listed in Table 1. They were se-lected for evaluation purposes rather than to mimic aparticular physiological motion profile.

RESULTS

Image Quality Comparison

The operation of the motion stage did not affect MRimage quality. The results of the SNR analysis areshown in Table 2. The signal, noise, and SNR areinvariant with respect to the operation of the motionstage. Images of a moving phantom are shown in Figure2. The three images shown are representative of the 120images acquired with the cardiac-gated GRE sequence.No artifacts due to electronic interference or view-to-

Table 1Parameters of the Prescribed Waveforms and the Root-Mean-Square (rms) and Maximum Deviations of the MR Displacementand Velocity Measurements*

Waveform Segment DT (msec) v (cm/sec) a (cm/sec2) DDrms (mm) DDmax (mm) Dvrms (cm/sec) Dvmax (cm/sec)

I 1 270 14.4 0.0 0.24 0.50 0.46 0.642 600 247.9 0.88 2.04 1.14 2.573 270 214.4 0.0 0.60 1.12 0.51 0.884 600 47.9 0.87 2.18 1.22 3.33All 0.78 2.18 1.02 3.33

II 1 200 7.2 0.0 1.07 1.18 0.40 0.442 150 47.9 0.70 1.10 0.23 0.303 150 14.4 0.0 0.47 0.65 0.53 0.664 450 247.9 0.68 1.44 1.56 3.415 200 27.2 0.0 0.89 1.13 0.95 1.636 150 247.9 0.49 0.87 1.80 2.107 150 214.4 0.0 0.59 0.79 1.44 1.718 450 47.9 0.47 0.93 1.93 4.40All 0.71 1.44 1.47 4.40

*Each waveform is divided into segments of constant velocity or constant acceleration. The rms and maximum displacement errors (DDrms andDDmax) and velocity errors (Dvrms and Dvmax) were calculated from the data presented in Fig. 4. The largest errors always occurred duringperiods when the motion stage changes direction, ie, segments 2 and 4 in waveform I and segments 4 and 8 in waveform II. They were due tomechanical backlash.

Table 2Signal, Noise, and Signal-to-Noise Ratio (SNR) Measured in (A) theAbsence of the Motion Stage and (B) With the Motion Stage Presentand Running

ConfigurationMean phantom

ROI valueNoise value

in airSNR

A 197.6 8.0 24.8B 197.8 8.0 24.8

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view motion inconsistencies were observed in theseimages.

Calibration

The results of motion stage calibration (linear displace-ment as a function of motor rotation) are shown in Fig.3. The overall correlation coefficient, K, for the entiredata set was found to be 4.794 6 0.003 cm/rev(mean 6 standard error) with a coefficient of determina-tion R2 5 0.99996. The correlation coefficient did notdepend on prescribed motion profile, nor did it dependon whether the motion stage was inside or outside thescanner. Since the stepping motor has a resolution of4000 steps per revolution, the lower limit on displace-ment precision is 0.0012 cm. In practice, the uncer-

tainty in the calibration coefficient (#0.1%) dominatesthe precision of the motion stage.

Motion Profile Validation

The displacement and velocity measurements for themotion profiles described in Table 1 are shown in Fig. 4.The prescribed motion profiles agreed with the MRdisplacement measurements obtained from the gatedGRE sequence as well as the motion sensor measure-ments (Fig. 4a,c). As listed in Table 1, the root-mean-square (rms) deviation between the MR-derived and theprescribed displacements was #0.08 cm. The maxi-mum deviation was 0.22 cm and occurred when themotion stage changed direction and was due to mechani-cal backlash of the rack and pinion and the platformassembly. These discrepancies are denoted by arrows inFig. 4a and c.

Good agreement was also observed between the cinePC-derived and the prescribed velocities (Fig. 4b,d). Therms and maximum deviations were #1.47 and 4.4cm/sec, respectively. Again, maximum deviation wereobserved at changes in direction and were due to themechanical backlash (arrows in Fig. 4b,d).

DISCUSSION AND CONCLUSION

We have constructed a motion stage that can accuratelygenerate 2D motion with high accuracy, precision, andreproducibility. The validation study has demonstratedthat on average the displacement is accurate to within0.08 cm and velocity is accurate to within 1.47 cm/sec.From our experiments, the mechanical backlash wasestimated to be 0.22 cm. However, it is possible tocompensate for this mechanical backlash using a soft-ware correction (9). Fortunately, for many in vitro mo-tion experiments, the relatively small displacement er-

Figure 2. The images of a phantom at different positionsduring a motion cycle. The phantom started at (a) (v 5 0cm/sec), moved across the center of FOV at (b) (v 5 14.4cm/sec), and stopped at (c). It then reversed the direction andreturned to a. Images were acquired with a prospectively gated2D GRE sequence. The noise level of these images was thesame; however, the phantom signal during the first severalphases was higher than that of the later phases due tomagnetization re-growth during the trigger window.

Figure 3. Calibration of linear displacement versus motorrevolution using various motion profiles. The open circles areobtained using one set of velocity and acceleration values butvarying the total distance. The open squares are obtainedusing various velocity and acceleration values. The solidsquares represent calibrations done in the scanner.

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ror caused by backlash (,0.2 cm) is unlikely to be amajor concern, since it occurs in every motion cycle.

While this evaluation was carried out using motionprofiles with a maximum velocity of 14.4 cm/sec, testshave shown that repeated motion (at 60 cycles/min)with maximum velocity of 28.8 cm/sec and a maximumacceleration of 144 cm/sec2 is achievable with a 2 kgphantom. It is also possible to prescribe motion wave-forms more complex and physiologically relevant thanthe ones used in this evaluation. Finally, the modularityof this motion stage makes future extensions possible.For example, in these measurements a slotted platewith linear trajectory at 45° were used. Other slotconfigurations are possible, including curved slots. Ro-tation could be accomplished by converting linear mo-tion into rotation. This motion stage may be used in avariety of experiments, such as studying the sensitivityof pulse sequences to myocardial motion and evaluatingmotion artifact correction schemes. In addition, thesimulation of cardiac motion during MR measurementof coronary flow can be achieved by attaching a flowphantom (9) to the motion stage and programming asimulated cardiac motion profile.

ACKNOWLEDGMENTS

The authors acknowledge the efforts and comments ofLance J. Levendowski, M.S., Charles A. Mistretta, Ph.D.,Dana C. Peters, M.S., Lee N. Potraz, and Kristin L.Wedding, Ph.D., during the initial design and construc-tion phases of this project. The authors thank RebbeccaN. Stuckman, B.S., for implementing and evaluating theslotted-plate design and William E. Grogen, M.S., forproviding the motion sensors.

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Figure 4. Results of motion profile validation for waveforms I and II. a: Comparison of the prescribed displacement (solid line),the MR displacement measurements (open circles), and the motion sensor measurements (solid triangles) for waveform I. b:Comparison of the prescribed velocity (solid line) and the measurements from the cine PC MR images (solid squares) for waveformI. c,d: Corresponding results for waveform II. The numbers correspond to the segments listed in Table 1. The arrows highlight themotion direction changes, which result in maximum deviations between the measured and prescribed values due to mechanicalbacklash (see text). The error bars represent measurement uncertainties, which are described in text.

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