Path Length as a Metric for Subject Motion J.M. Ollinger 1 , T.R. Oakes 2 , F.B. Haeberli 1 , A.L. Alexander 1 , R.J. Davidson 1 Abstract SNR values were observed to decrease linearly when plotted against a path-length metric. Moreover, it decreased more rap- idly for a 70 degree flip angle than for a 90 degree flip angle. Further investigation shows that the variance of motion-induced signal changes can be modeled as the product of the variance of the through-slice displacement and a scale factor and that this scale factor can be approximated analytically. A model for SNR was used to estimate the motion sensitivity at flip angles of 70 and 90 degrees as well as the variance of the pulsatile motion. The fitted values are consistent with analytic results that suggest a minimum in the sensitivity to motion at approximately 70 degees and a relatively constant sensitivity at lower flip angles. Recent work by Bodurka et al. [1] shows that lower flip angles do not degrade temporal SNR. This work suggests that low flip angles do not reduce sensitivity to motion, but that motion sensitivity does increase rapidly for flip angles greater than the 70 degrees. Introduction Subject motion is a signficant source of noise in fMRI studies, particularly with juvenile subjects. Not only does it cause mis- alignment of the data but it also spoils the steady-state of the magnetization. Image misalignment can be corrected, but loss of steady-state and its restoration induces signficant uncorrected noise. As a result, subjects with excessive motion must often be excluded. Unfortunately, there is no agreed-upon quantitative metric for “excessive” motion. One potential quanti- tative metric is temporal SNR, which is strongly correlated with within-subject t-statistics. The work presented here is based on the observation that SNR is strongly correlated with path length, where path length is defined as the distance traversed by a point 5cm from an arbitrary center of rotation (the one used by the motion-correction software). This variable is easily com- puted from position estimates provided by the motion-correction software. Further analysis showed that these data are far more interesting. The proposed path-length metric is linearly related to the standard deviation of the through-slice displacement because each step follows a Rayleigh distribution. Moreover, it can be shown that under certain assumptions, the contribution of motion to the image variance is linearly related to this through-slice motion variance. Finally, SNR data from large studies can be used to estimate these parameters directly. Bodurka and Ban- dettini [1] showed that temporal SNR is relatively unaffected by lowering the flip angle. This work complements that work by showing how reduced flip angles affect the sensitivity of SNR to subject motion. Data Data from three existing studies were used: brdevel: 45 normally developing 11-15 year old children performing an event-related go-nogo task. Each subject was scanned up to four times in separate sessions for a total of 209 sessions. Two runs of either 132 or 145 frames were ac- quired. autism: 46 autistic and control subjects 9-23 years old performing an event-related face/voice task. Two runs of 222 frames were acquired. Tools: 40 adult controls performing an event-related button-press motor task. One run of 144 frames was collected. These data were acquired with an earlier version of the scanner hardware and software than the other two studies. Data Acquistion EPI images were acquired on a GE 3T Signa scanner using a quadrature coil with TE=30ms, TR=2s, flip angle of 90 de- grees for tools and autism, 70 degrees for brdevel. 30 slices with a 4mm width,1mm gap were acquired. The RF pulse was the spectral-spatial pulses included in version ESE12 of the EPI sequence. Data Analysis SNR and path length: Temporal SNR was computed for the EPI data sets after reconstruction, detrending, and motion cor- rection using Fourier interpolation with AFNI’s 3dvolreg program. Path length was found by first computing the position of an arbitrary point 8.7 cm from the center of rotation (i.e., 5cm along each axis). The change in position at each frame was then computed and their absolute value was summed to yield path length. The variance of the motion was computed by taking the variance of these position changes. Regression Analysis. The expression in Equation (3) was fit to the observed data using the Levenberg-Marquardt algorithm to minimize an unweighted least squares objective function. Bootstrap estimates of the mean-square error of the estimates were computed using 1000 resamplings. SNRI 0 was set to a fixed value of 250 based on the observation that the temporal SNR in human subjects is rarely greater than this, even when comparing coils that yield large SNR improvements in phan- toms. Sensitivity of the results to this parameter were calculated by repeating the fit for a range of values. Subjects from the tools study were not included in this analysis because they were acquired two years earlier under an ear- lier version of the GE operating system. Computation of gm/s: The motion sensitivity term g m /s was computed using the Stanford Bloch equation simulator [2] to com- pute the steady-state magnetization and the flip angle for the spectral-spatial pulse used by the scanner. The integral in Equation (2) was evaluated over the central lobe of the slice profile. Conclusions: The observed relationship between path-length (and correspondingly the motion variance) and SNR suggests that path- length can be used as a proxy for SNR. Moreover, the model given by Equation (3) fits these data well. The computed motion sensitivity reaches a minimum at 70 degrees and is relatively flat for low flip angles. This results from the decrease in signal at low flip angles and, to a small extent, to the longer time it takes for the magnetization to recover steady-state at small flip angles. The standard deviation of the pulsatile motion was .147 mm. In the tools study (of young adult controls), the standard deviation of rigid-body motion was .055 +/- .032 mm. This suggests that involuntary motion may be a significant contributor to the noise for data with little observable motion. The insensitivity to the maximum achievable SNR (SNR 0 ) suggests that the SNR loss associated with parallel imaging would have little effect on the observed SNR. The analytic value of the motion sensitivity depends strongly on the range of integration in Equation (2). A much steeper falloff of motion sensitivity with decreased flip angle is predicted if the integral is carried out over the entire support of the simulated slice profile. It is assumed here that the actual signal is band-limited and falls off rapidly outside the first null of the slice profile. Finally, the shape of the motion sensitivity curve depends strongly on the characteristics of the RF pulse and will not necessarily generalize to other pulses. Indeed, the methodology presented here can be used to optimize choices for pulse type, slice thickness and slice spacing. References: 1. Bodurka, J. and Bandettini, P, (2009) “Physiological Noise Effects on the Flip Angle Selection in BOLD fMRI,” Proc. Intl. Soc. Mag. Reson. Med. 17. 2. Hargreaves, B., Bloch Equation Simulator from the Stanford Magnetic Resonance Systems Lab, www-mrsrl.stanford.edu 1.The Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin-Madison. 2. The Henry Jackson Foundation, Bethesda MD. Results Support This work was supported by the following NIH grants: MH067167, MH069315, DA15879, MH069315, MH084051, HD003352, and MC222895 0 20 40 60 80 100 120 140 160 3 30 Path Length (mm/100 frames) SNR 0 20 40 60 80 100 120 140 160 5 50 Autism Tools Path Length (mm/100 frames) SNR 0 20 40 60 80 100 120 140 160 0.0 0.2 0.4 0.6 0.8 1.0 SNR Standard Deviation of Motion (mm) brdevel Flip angle: 70° g m /s: .0382 +/- .0018  pm : .1355 +/- .0094 0 20 40 60 80 100 120 140 160 0.0 0.5 1.0 1.5 2.0 SNR Standard Deviation of Motion (mm) Autism Flip angle: 90° g m /s: .0360 +/- .0025  pm : .1591 +/- .0169 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 B1 max (Gauss) Motion Sensitivity (g m /s) Relative Signal Strength Motion Sensitivity Signal 90° flip angle y 0.00 0.01 0.02 0.03 0.04 0.05 0.0 0.1 0.2 0.3 0.4 200 300 400 500 600 700 sigma_pm brdevel sigma_pm autism gms brdevel gms autism Baseline SNR Estimated Motion Sensitivity g m /s Physiological Component of Noise ( pm )  pm - brdevel  pm - autism g m /s - brdevel g m /s - autism Linear regression of SNR values against the standard deviation of the motion shows a strong correlation (R 2 =.76 for brdevel and R 2 =.84 for autism). The slope for brdevel data at a flip angle=70 degrees is 13.5% higher than that for the autism data at a flip angle of 90 degrees. This change in slope with flip angle suggests that data acquired at the lower flip angle are more sensitive to motion. Nonlinear fits to the same data plotted against standard deviation show that the model in Equation (3) fits the data well. The fitted value for pulsatile motion differed by 17.4 +/- 12.1% with a mean value of 0.147 mm. The motion sensitivity parameter, g m /s, increased by 6.1 +/- 8.8% when the flip angle was decreased from 90 degrees to 70 degrees. The effect of increasing the assumed value for SNR 0 is shown at left. A 100% change of SNR 0 from 300 to 600 de- creased estimates of the motion sensitivity g m /s by 3.5% while increasing those for σ pm by 13%. This suggests that the model and hence the observed SNR is not strongly affected by the maximum achievable SNR once it exceeds a certain a value. That value is determined by the magnitude of the physiological noise. Values of the motion sensitivity computed using Equation (2) are shown at right. The sensitivity to motion increases sharply for flip angles above 80 degrees and reaches a mini- mum for a flip angle of 70 degrees. This curve predicts a 29% decrease in motion sensitivity for a flip angle change of 90 to 70 degrees rather than the estimated 6.1% increase. However the curve was computed under the assumption of a uniform B1 field. In practice, dielectric effects and coil sensi- tivities cause varying flip angles across the brain. Since di- electric effects tend to decrease the flip angle at the edges of th brain, it is possible that much of the brain experienced a flip angle change of 80 to 60 degrees, which would cause an increase in the motion sensitivity of 8.1% R to subject motion. SNR = s  T 2 +  phys 2 +  m 2 Noise due to motion Physiological noise Thermal noise hermal noise h Th Th SNR = 1  T 2 s 2 +  phys 2 + g m 2 s 2  z 2 +  pm 2 ( ) g m 2 = b N  i  1 sin  z  z s ( ) ( ) w /2 w /2  M z z , t i ( ) z dz i =0 N  1  2 where is the standard deviation of the physiological noise, is the variance of the pulsatile motion, and s  pm  pm 2 rforming an event-related go-nogo task. Each subject was 209 sessions. Two runs of either 132 or 145 frames were ac - orming an event-related face/voice task. Two runs of 222 frames n-press motor task. One run of 144 frames was collected. These hardware and software than the other two studies g m 2 = b N  i  1 s i n  z  z s ( ) ( )  w / 2  z i  z d z i = 0  SNR = 1 1 SNR 0 2 + g m s              2  z 2 +  pm 2 ( )                  1 2 Theory Assuming that thermal noise, physiological noise, and noise due to motion are statistically independent leads to the expression for temporal SNR given at the right. Methods Assume further that the physiological noise can be split into BOLD components and non-BOLD components. BOLD components (s 2 α 2 phys ) consist of any signal that modulates T 2 * but is not a signal of interest. Non-BOLD physiological noise (σ 2 pm ) is assumed to consist of pulsa- tile motion. It can be shown that the component due to the through- slice displacement caused by subject motion can be ap- proximated by the product of the variance of the motion itself and a motion sensitivity term, g m 2 , describing the sensitivity of the pulse sequence to subject motion. A more succinct expression for SNR that can be fit to the observed data is formed by combining terms as shown at right. The thermal and physiological noise compo- nents are lumped into a single term, SNR 0. (2) (1) (3) brdevel Flip angle = 70 degrees slope = -36.9 intercept = 193 Autism Flip angle = 90 degrees slope = -32.5 intercept = 180 View publication stats View publication stats