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Extraction of Temporal Information in Functional MRI Manbir Singh, Senior Member, IEEE, Witaya Sungkarat, Jeong-Won Jeong, and Yongxia Zhou
Abstract—The temporal resolution of functional MRI (fMRI) is limited by the shape of the hemodynamic response function (hrf) and the vascular architecture underlying the activated regions. Typically, the temporal resolution of fMRI is on the order of 1 s. We have developed a new data processing approach to extract temporal information on a pixel-by-pixel basis at the level of 100 ms from fMRI data. Instead of correlating or fitting the time-course of each pixel to a single reference function, which is the common practice in fMRI, we correlate each pixel’s time-course to a series of reference functions that are shifted with respect to each other by 100 ms. The reference function yielding the highest correlation coefficient for a pixel is then used as a time marker for that pixel. A Monte Carlo simulation and experimental study of this approach were performed to estimate the temporal resolution as a function of signal-to-noise ratio (SNR) in the time-course of a pixel. Assuming a known and stationary hrf, the simulation and experimental studies suggest a lower limit in the temporal resolution of approximately 100 ms at an SNR of 3. The multireference function approach was also applied to extract timing information from an event-related motor movement study where the subjects flexed a finger on cue. The event was repeated 19 times with the event’s presentation staggered to yield an approximately 100-ms temporal sampling of the hemodynamic response over the entire presentation cycle. The timing differences among different regions of the brain activated by the motor task were clearly visualized and quantified by this method. The results suggest that it is possible to achieve a temporal resolution of 200 ms in practice with this approach. Index Terms—Functional MRI, motor activity, temporal resolution.
I. INTRODUCTION
B
LOOD-OXYGENATION-LEVEL-DEPENDENT (BOLD)based functional MRI (fMRI) has now become the modality of choice to conduct human brain mapping studies at a routinely available spatial resolution of 2–3 mm and a temporal resolution of 1–2 s [1]. The BOLD effect originates within the microvasculature, which is presumably colocalized with neuronal activity, though there is an ongoing debate on whether the fMRI BOLD signal is a true reflection of neuronal activity [2]. Consistent with high-resolution optical imaging, which suggests a prompt stimulus-related increase in the level Manuscript received December 13, 2001; revised July 19, 2002. This work was supported in part by Grants NIA-NIH P50 AG05142 and NIH-MH RO1 53213. M. Singh is with the Departments of Radiology and Biomedical Engineering, University of Southern California, Los Angeles, CA 90089-1451 USA (e-mail:
[email protected]). W. Sungkarat, J.-W. Jeong, and Y. Zhou are with the Department of Biomedical Engineering, University of Southern California, Los Angeles, CA 90089-1451 USA (e-mail:
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/TNS.2002.803774
of deoxyhemoglobin within the microvasculature [3], a negative BOLD signal—the so-called fast response—has been detected by some investigators approximately 2 s after the stimulus [4]. If detection of the fast response can be established in fMRI, it would provide means to localize the activation sites within the microvasculature at a resolution of about 1 mm and presumably improve the temporal resolution. However, the origin of the fast response is not well understood at this time, and its detection at 1.5 T is still controversial [5]. Detection of the positive BOLD signal remains the standard for most fMRI studies. A practical limitation of positive BOLD fMRI is that the signal is not confined to the microvasculature, but spreads into veins that drain blood from the activated brain tissue, and these draining veins may be several millimeters or up to a centimeter away from the actual site of neuronal activation. Thus, identification of the actual site of activation and its temporal behavior, i.e., the spatiotemporal resolution of BOLD fMRI, is limited not only by the hemodynamic response characteristics but also by the vascular architecture. The spatiotemporal resolution depends critically on how well one can separate the microvasculature from the relatively large draining veins, especially at the field strength of 1.5 T used in this work where the signal from large vessels could be a factor of 5–10 higher than the signal from the microvasculature [6]. The temporal response of the BOLD signal is modeled by a so-called hemodynamic response function (hrf) [7], and though the hrf exhibits a relatively slow peaking time of about 3–5 s, temporal shifts on the order of 1 s or shorter have been extracted from activated regions. For example, Kim et al. [8] reported that using an activated visual area as a time-reference for a visually cued motor study, the limit to detect delay between a motor-activated area with respect to the visual cue was about 2 s. In another study, Wildgruber et al. [9] used a sliding step function as a reference function to find the temporal delay between two regions of interest (ROI), where one ROI enclosed the supplementary motor areas (SMAs), and the other enclosed the primary motor areas (PMAs). The results for seven subjects 1.6 s within suggest a mean delay time or latency of 3.0 s 1.6 s within the PMAs with respect to the SMA and 3.8 s movement onset. The temporal delay between the SMA and the PMA is consistent with evoked potential studies [9]. However, relatively large ROIs were used in [9], leading to an averaging of the timing information from different micro- and macrovasculature signals spread over relatively large portions of the brain. To avoid the inherent loss in timing resolution when several pixels are averaged within an ROI, the objective of the work reported here was to extract timing information individually from each pixel. A Monte Carlo study was conducted to establish
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SINGH et al.: EXTRACTION OF TEMPORAL INFORMATION IN fMRI
limits on the temporal resolution as a function of SNR in the time-course data of each pixel. Experimental data were then used to verify the Monte Carlo estimates. Consistent with the suggested limits of the temporal resolution, a technique was developed to track the BOLD signal at a temporal resolution of 200 ms on a pixel-by-pixel basis as the signal propagates through the vasculature. Since the cumulative delay between the microvessels and the macrovessels is on the order of 1 s [10], [11], tracking at 200-ms temporal resolution can be used to separate the microvasculature from the relatively large blood vessels. This procedure not only results in better localization of the activated sites, but also enables temporal relationships among different brain regions to be determined based on the onset time of activation of a pixel within selected clusters of activated pixels. The Monte Carlo simulations and results of a motor study where we used tracking to visualize and quantify the spatiotemporal relationships among several activated regions of the human brain are presented in this paper.
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Fig. 1. (a) Temporal sampling of the hrf by combining samples from multiple trials. As an example, the time-points when slice 1 is acquired are shown by open circles. (b) Plot of the interval between successive temporal samples. This interval is under 200 ms for almost all samples and under 100 ms for a majority.
II. METHOD Event-related fMRI studies were conducted during a finger flexion task for three normal human volunteers. The subjects were instructed to flex either the right index finger (for two right-handed males) or the left index finger (for one left-handed female) and place it on a response button fiber-optically coupled to a computer. Upon hearing a verbal cue, the task was to immediately press the button (thereby, electronically marking the initiation time of the movement), unflex the finger, and then return to the original position with the flexed finger resting on the button. The subjects were trained before entering the magnet to press the button, unflex, and return to the original position in a smooth motion in approximately 700 ms. The timing of the cue was randomized to produce a mean of 15 s with a standard deviation of 2 s, i.e., the inter stimulus interval (ISI) was 15 2 s. A GE 1.5 T LX 8.3 EPI system, equipped with a quadrature head-coil and gradients of strength 25 mT/m and 125 T/m/s slew rate, was used to acquire time-series data with TR = 1.2 s, effective TE = 45 ms, 90 flip angle, 64 128 acquisition matrix, 20 40 cm field-of-view, and number of excitations (NEX) = 1. A total of 250 images were acquired per slice from two 8-mm-thick contiguous transaxial slices covering a substantial portion of the motor regions. The total acquisition time was approximately 5 min and contained 19 cued flexions. After registration [12], the fMRI data were processed by correlating the time-course of each pixel to a series of reference functions. The stimulus presentation sequence was modeled in steps of 700-ms-wide rectangular pulses and convolved with a model of the hrf [7] at a high temporal sampling rate of 10 ms and then down-sampled at time-points corresponding to the actual image acquisition time per slice, yielding a different reference function for each slice. We refer to this reference function as the zero-delay reference function. Because of the jittering in the ISI, the actual time at which the hrf was sampled (i.e., the slice acquisition time) was staggered from trial to trial with respect to the hrf. Assuming a stationary hrf following each finger-movement trial, a plot of the hrf and the
1 = 400
Fig. 2. Example of four reference functions with t ms. In the actual studies, t and 100 ms were used. Only the first four lobes of the 19-lobe reference functions are shown here for clarity. Notice that in addition to the shift in the peak position, the shape of the reference function also changes with t.
1 = 200
1
different times at which it is sampled throughout the acquisition sequence are presented in Fig. 1. It is apparent that almost the entire hrf is sampled in less than 200-ms time intervals with a significant sampling below 100 ms, suggesting that a temporal resolution of approximately 200 ms would be consistent with Nyquist sampling. Tracking of the BOLD signal per pixel was achieved by correlating the time-series of each pixel to a series of reference functions per slice. These reference functions were generated before by shifting the convolved response in steps of was 100 ms for the simulation and resampling, where validation study and 200 ms for the pixel-tracking study described below. Note that this procedure is not equivalent to the commonly used procedure of shifting a given reference function to model delay. In our approach, not only the position of peaks but the entire shape of the reference function is subject in accordance with the shape of to change as a function of the hrf. An example of a partial series of reference functions ms is composed of four reference functions with presented in Fig. 2. Each reference function within a series of reference functions is a marker of a specific time delay, i.e., latency with respect to the stimulus onset time. The time-series of every pixel in each slice was then correlated with the reference functions, and through a logic test, each pixel was assigned to that reference function that produced the highest correlation coefficient (CC). The latency of each pixel was, thus, represented by the delay of the reference function producing the highest CC value.
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Fig. 3. (Top three rows) Experimental time-courses from three pixels activated in the finger movement protocol. The SNR in these time-courses are (top to bottom) 4.26, 1.84, and 1.25, respectively. The bottom row shows a simulated time-course at SNR = 4.0.
A. Monte Carlo Simulation A simulation study was conducted to estimate the limit on extracting temporal information as a function of SNR in the time-course of a pixel where the SNR is defined as the ratio of peak signal height to the standard deviation in the baseline. The simulation relied on the protocol used to acquire data for the finger flexion study described above. The convolved hrf was shifted in steps of 100 ms and resampled at time-points corresponding to the slice acquisition time to form a series of 61 reference functions per slice. The reference functions, thus, span a time shift of 3 s with respect to the zero-delay reference function (where the zero-delay reference function represents no additional delay except that inherent to the peaking time of the hrf with respect to the onset of the stimulus). These reference functions also represent noise-free time-courses at specific delays. It is well known that there are two main sources of noise in fMRI—physiological noise and electronic noise—and the net noise is a quadrature summation of the two. The physiological noise is a function of the precession frequency , whereas the . The physiologic noise repelectronic noise is a function of resents fluctuations in the hemodynamic response of the brain from respiration and pulsations due to cardiac, cerebrospinal fluid (csf), and vascular motion. Any overlap in the physiologic frequencies or their aliases with the stimulus presentation frequencies can lead to the so-called “physiological artifacts” in fMRI [13], [14]. The effect of electronic noise was simulated by adding random Gaussian white noise to the noise-free convolved hrf to achieve an SNR between 1–10. Typically, the BOLD signal represents a 1%–5% increase in signal intensity from the baseline, and baseline fluctuations are approximately 0.5%–1%. Thus, the SNR is typically in the 1–10 range, where the higher SNR values are for signals originating from veins and lower values from the microvasculature [6]. After adding electronic noise, the convolved hrf was down-sampled at a time-point lying midway between two
IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 49, NO. 5, OCTOBER 2002
Fig. 4. Plot of the standard deviation (std) in milliseconds from 10 000 trials of a Monte Carlo study, indicating the uncertainty in determining the temporal delay of a pixel as a function of SNR in its time-course. TABLE I COMPARISON OF EXPERIMENTALLY DETERMINED STANDARD DEVIATION (exp) IN MILLISECONDS, TO THAT OBTAINED FROM THE MONTE CARLO SIMULATION (sim). THE SNR1 AND SNR2 DENOTE SNRs FOR THE TWO PIXELS IN EACH PAIR
reference functions to obtain a time-course simulating the worst case scenario where the delay of a pixel might lie exactly between two reference functions. Physiological noise was added to this time-course by a sinusoidal function at the primary frequency of the stimulus presentation sequence. The sinusoidal function was estimated from experimental data by comparing the power spectra of the time-courses of 100 activated pixels lying within the PMA (referred to as set 1) to the power spectra of 100 pixels lying within gray and white prefrontal brain regions where no activity was expected during finger movements (set 2). It was found that for an average SNR = 2.0 in the time-courses of the PMA-activated pixels, the ratio of the power between set 2 and set 1 pixels at the primary stimulus frequency ranged from 0.05–0.2. Accordingly, the amplitude of the sinusoidal function was selected randomly such that, after repeated trials, the ratios of the sinusoidal power to that of the time-course (after adding noise) at the primary stimulus frequency were distributed uniformly between 0.05 to 0.2. The phase of the sinusoidal function was also assigned and for each trial. For simulating randomly between time-courses at different SNRs, the amplitude of the sinusoidal
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Fig. 5. Selected frames 400 ms apart showing the spatiotemporal relationships among pixels activated within the SMA, PMA, and SA during the finger movement experiment for subject1. The subject moved his right finger.
function was scaled appropriately to conform to the selected SNR. The process of adding random Gaussian and physiological noise was repeated 10 000 times to simulate 10 000 samples of time-courses per SNR. The temporal delay for each sample was then computed from the series of reference functions, and the standard deviation in the 10 000 delay values was used as the estimate of the expected uncertainty in the delay.
B. Experimental Validation Study A human study was conducted to validate the Monte Carlo simulations. Using the same MRI pulse sequence and protocol as described above, the subject performed a cued flexion of the right index finger 19 times to complete one experiment in 5 min. Then the experiment was repeated seven more times during the same MRI scanning session to obtain data from a total of eight trials. These fMRI data were processed as before using a series of reference functions spaced 100 ms apart to determine the delay of each activated pixel with respect to the zero-delay reference function in each experiment. Then, the relative delay or temporal shift between a pair of pixels (where one pixel was selected from the left motor area and the other from the right motor area) was determined separately from the eight experiments, and the standard deviation in the eight temporal-shift values was compared to the Monte Carlo-computed standard deviations at the experimentally estimated SNR. This process was repeated for several pairs of pixels. The temporal
shift between two pixels, instead of the actual delay of a pixel with respect to the zero-delay reference function, was used to avoid any systematic errors due to our lack of knowledge about the precise MR slice acquisition time with respect to the button press time. C. Pixel-Tracking Study To demonstrate that the BOLD signal could be tracked on a pixel-to-pixel basis, data from three human volunteers were processed by a series of 41 reference functions per slice that were of 200 ms and spanned a range of 4 s with spaced by respect to the zero-delay reference function. The longer range was used to enable tracking of pixels in the supplementary, primary, and sensory areas, which may be several seconds apart, and the 200-ms interval was selected to reduce the computation values could be used in the future. Also, instead time. Shorter of assigning a pixel to only that reference function that produced the highest CC, a pixel was assigned to all reference functions whose CC values with respect to the pixel’s time-course were within 1% of the maximum value. This 1% tolerance is consistent with the 200–ms spacing because the CC is reduced by approximately 1% between two reference functions when one is displaced 200 ms with respect to the other. In addition, the tolerance allows a pixel to persist through different delays or disappear and reappear through the activation time sequence, both of which may occur in practice. Pixels whose CC values ) exceeded a threshold of 0.3 (corresponding to were displayed in image frames as a function of .
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Fig. 6. Selected frames 400 ms apart showing the spatiotemporal relationships among pixels activated within the SMA, PMA, and SA during the finger movement experiment for subject2. The subject moved her left finger.
III. RESULTS Examples of time-courses from three activated pixels in a typical human study, where one pixel was within the PMA (SNR = 4.26), the second within the SA (SNR = 1.84), and the third within the SMA (SNR = 1.25), are shown in the top three rows of Fig. 3, and a typical Monte Carlo-simulated time-course at SNR = 4.0 is shown at the bottom. The simulated data appear very similar to the experimental data. The results of the Monte Carlo study to estimate the uncertainty (i.e., the standard deviation) in the temporal delay of a pixel are plotted in Fig. 4 as a function of the SNR in the pixel’s time-course. The results show that the uncertainty or temporal resolution ranges from about 350 ms at SNR = 1 to about 50 ms at SNR = 10. The 50-ms limit is due to our assumption that the event occurs exactly midway between two reference functions and represents a worst case scenario. The results of the experimental study, where the standard deviation from eight experiments was compared to the Monte Carlo simulation, are presented in Table I for eight representative pixel pairs. The experimental standard deviation arises from the difference between two time-courses whose to SNR values are labeled SNR1 and SNR2. To relate and the simulated value (sim), the standard deviations corresponding to SNR1 and SNR2 were estimated from Fig. 4 and added in quadrature to obtain sim . The experimental standard deviations are in good agreement with Monte Carlo simulations. Our assumption that events occur
exactly midway between two reference functions could increase the simulated standard deviation by as much as or about 70 ms, and it is seen that most of the simulated values are higher than the experimental values consistent with this explanation. Examples of pixel tracking for two different subjects, where subject1 moved his right index finger and subject2 moved her left index finger, are presented in Figs. 5 and 6, respectively. ms reference Though this study was conducted with functions, selected images corresponding to reference functions ms are shown for lack of space. or frames delayed by The spatiotemporal relationships among different regions of the brain are visible in these images. These relationships are best depicted by a movie where one can actually visualize the path of the BOLD signal as it propagates through the vasculature. The results from all three subjects show that various SMAs are activated first, followed by the contralateral and ipsilateral PMAs, and then the SAs. The start of activation at certain locations (referred to as activation nodes) followed by propagation of the activation through regions that geometrically and anatomically conform to veins can be seen from individual frames. The frames also reveal that activation within large veins is delayed by several seconds with respect to the activation nodes, which is consistent with previous studies [10], [11]. Using the metric “ ” to quantify activation, where average -score the number of pixels (the -score is defined as the difference between the average pixel intensities during the activation and baseline conditions, divided by the standard deviation of the baseline intensities), the onset
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Fig. 7. (a) Clusters in the SMA and plots of corresponding activation metric “A” defined in the text. (b) Clusters in the PMA and plots of corresponding activation metric “A” defined in the text. (c) Clusters in the SA and plots of corresponding activation metric “A” defined in the text.
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time, and the peaking time of all activated clusters (where a cluster was defined by a minimum of four contiguous pixels) were determined to quantify their temporal relationships. An example of this analysis for subject2 is presented in Fig. 7. The activated SMA clusters lying within both hemispheres of the brain are shown in the image displayed at the top in Fig. 7(a). This image is derived from a composite of all frames. The various SMA regions have been labeled R1–R4 for the right hemisphere and L1–L2 for the left hemisphere. The plots of the metric “ ” within each cluster as a function of latency are shown below the image. These plots group the latencies of pixels within each cluster. Latencies corresponding to the cluster onset time (which is presumed to correspond to activation within the microvasculature) or the peaking time (which should correspond to activation within a relatively large vein) can be obtained from these plots. Similar clusters and plots of “ ” in the PMA and SA are shown in Fig. 7(b) and (c), respectively. Since the microvasculature is presumed to underlie regions of neuronal activity, the delays between cluster onset times should reflect the temporal relationship between regional neuronal activity. As an example of determining temporal shifts between two activated regions, we computed the delay between the first activated cluster in the SMA and the first activated cluster in the PMA. The latency of the onset time of the first SMA cluster L1 in Fig. 7(a) is 2.9 s, and the latency of the first PMA cluster R4 in Fig. 7(b) is 3.5 s, suggesting a temporal delay of 600 ms between these regions. Similar plots for the other two subjects indicated delays of 1100 and 1000 ms, respectively. These delays are consistent with previous fMRI and evoked potential studies [9]. In addition to the first-activated SMA and PMA pixels, several other clusters within the SMA, PMA, and SA are activated in fMRI as seen in Figs. 5–7. This work provides a tool to measure the temporal delays among regions, based on the assumption that the timing of neuronal activity is correlated to the onset timing of pixels within a cluster. IV. CONCLUSION The temporal resolution in fMRI depends on the characteristics of the hemodynamic response, the vascular architecture, and the SNR in the time-course of pixels. By using a technique we developed, where a series of reference functions is correlated to the time-course of individual pixels, we have shown by Monte Carlo and experimental studies that it is possible to extract tem-
poral information on the order of 100 ms at an SNR of 3 in the time-course. As an application of the technique, we have presented results suggesting that individual pixels can be tracked at a temporal resolution of 200 ms in an event-related finger movement study. The tracking study shows temporal delays of 600, 1100, and 1000 ms, respectively, for three subjects between their earliest activated region within the SMA and the earliest activated region within the PMA. REFERENCES [1] R. S. Menon, J. S. Gati, B. G. Goodyear, D. C. Luknowsky, and C. G. Thomas, “Spatial and temporal resolution of functional magnetic resonance imaging,” Biochem, Cell Biol., vol. 76, pp. 560–571, 1998. [2] E. A. Disbrow, D. A. Slutsky, T. P. L. Roberts, and L. A. Krubitzer, “Functional MRI at 1.5 tesla: A comparison of the blood oxygenation level-dependent signal and electrophysiology,” in Proc. Natl. Acad. Sci., vol. 97, 2000, pp. 9718–9723. [3] A. Grinvald, R. D. Frostig, R. M. Siegel, and R. M. Bartfield, “Highresolution optical imaging of functional brain architecture in the awake monkey,” in Proc. Natl. Acad. Sci., vol. 88, 1991, pp. 11 559–11 563. [4] R. S. Menon, S. Ogawa, X. Hu, J. P. Strupp, P. Anderson, and K. Ugurbil, “BOLD based functional MRI at 4 tesla includes a capillary bed contribution: Echo-planar imaging correlates with previous optical imaging using intrinsic signals,” Mag. Res. Med., vol. 33, no. 3, pp. 453–459, 1995. [5] S. Lai, G. H. Glover, and H. A. Baseler, “Pseudo fast response in functional MRI,” Int. Soc. Mag. Res. Med, vol. 3, p. 1425, 1998. [6] J. S. Gati, R. S. Menon, K. Ugurbil, and B. K. Rutt, “Experimental determination of the BOLD field strength dependence in vessels and tissue,” Mag. Res. Med., vol. 38, no. 2, pp. 296–302, 1997. [7] M. S. Cohen, “A linear systems approach to the parametric analysis of fMRI time-series,” in Proc. Int. Soc. Magnetic Resonance in Medicine, 1997, p. 356. [8] S.-G. Kim, W. Richter, and K. Ugurbil, “Limitations of temporal resolution in functional MRI,” Mag. Res. Med., vol. 37, no. 4, pp. 631–636, 1997. [9] D. Wildgruber, M. Erb, U. Klose, and W. Grodd, “Sequential activation of supplementary motor area and primary motor cortex during self-paced finger movement in human evaluated by functional MRI,” Neuorosci. Lett., vol. 227, pp. 161–164, 1997. [10] A. T. Lee, G. H. Glover, and C. H. Meyer, “Distribution of large veinous vessels in time-courses spiral blood-oxygen-level-dependent magnetic resonance functional neuroimaging,” Mag. Res. Med., vol. 33, no. 6, pp. 745–754, 1995. [11] M. Singh, P. Patel, D. Khosla, and T. Kim, “Segmentation of functional MRI by k -means clustering,” IEEE Trans. Nucl. Sci., vol. 43, pp. 2030–2036, June 1996. [12] M. Singh, L. Al-Dayeh, P. Patel, T. Kim, C. Guclu, and O. Nalcioglu, “Correction of head movements in multi-slice EPI and single-slice gradient-echo functional MRI,” IEEE Trans. Nucl. Sci., vol. 45, pp. 2162–2167, Aug. 1998. [13] X. Hu, T. Le, T. Parrish, and P. Erhard, “Retrospective estimation and correction of physiological artifacts in fMRI,” Mag. Res. Med., vol. 34, pp. 201–212, 1995. [14] L. Al-Dayeh, T. Kim, W. Sungkarat, and M. Singh, “Multi-frequency reference function to reduce noise in functional MRI,” IEEE Trans. Nucl. Sci., vol. 46, pp. 513–519, June 1999.
