Optimum Stimulus Timing for Estimating fMRI Response Latencies R. M. Birn 1 , Z. S. Saad 1 , P. A. Bandettini 1 1 National Institute of Mental Health, Bethesda, MD, United States Synopsis : The purpose of this study is to determine, by simulation, the optimum stimulus design for estimating response latencies. The effect of two parameters were studied – the number of stimuli in a fixed amount of time, and the stimulus block duration. For time courses with an inter-stimulus interval that varies in time, the optimum number of stimuli was exactly half of the total number of time points acquired. A longer inter-stimulus interval of 8 seconds was optimal for a time courses with a constant ISI. The optimal stimulus block duration was between 4-6 seconds. Introduction : The design of optimal experimental paradigm timing is currently a central issue in fMRI. Recent studies have discussed the tradeoffs of involved with the detection of the relatively small hemodynamic changes, versus the characterization of their temporal response (1-3). Blocked designs, employing long stimulus durations and inter-stimulus intervals, are generally best for detection of small signal changes. In contrast, more rapidly varying event-related designs are better for estimating the temporal shape of the fMRI response. Recently, estimation of latency has been more commonly performed in fMRI studies. In this study we address the optimal design for estimating the latency of the hemodynamic response. The estimation of the response latency relies heavily on the transitions in the measured signal between the task and control states. It is therefore expected that stimuli with more frequent transitions and hence shorter block lengths will allow a better estimation of the response latency. A short stimulus duration, however, results in a smaller response, and a brief control period does not allow full recovery of the signal to baseline. These two opposite effects suggests that there is an optimal intermediate stimulus block duration. Methods : The efficiencies of various designs at estimating response latencies were computed by simulating multiple stimulus time series with either a constant or a varying inter-stimulus interval (ISI). All stimulus time series were convolved with a Gamma-Variate to simulate the hemodynamic fMRI response. 8192 instances of random Gaussian noise (with a standard deviation equal to ¼ of the maximal BOLD response) were added to each time course. The latencies were estimated using the Hilbert transform of the cross- correlation function (4). Finally, the standard deviation of the 8192 latency estimates was computed . The effect of two parameters were studied: the number of stimuli, and the stimulus block duration. In the first simulation, the number of 1s duration stimuli was varied from 16 to 176 in a 192-second run. In the second simulation, block sizes were varied from 2s to 32s, with an equal number of stimuli (96 stimuli). For runs with a varying ISI, 10 different randomized time series with a particular block size or stimulus number were generated. In all cases, the latency was fixed at 2s. Results : The standard deviation of the latency estimates for time courses with different number of stimuli, resulting in different ISIs, are shown in Figure A, and for different stimulus block durations is shown in Figure B. The lines represent stimulus time series with an ISI constant in time, and the o’s and +’s represent different time courses with an ISI that varies in time. Two different stimulus durations (SD) are illustrated in Figure A: 1s and 4s. For a varying ISI, the minimum standard deviation occurs for a stimulus design with exactly half of the time spent in either the task or control period, at an average ISI of 2s for a 1s duration stimulus. For a constant ISI, the minimum occurs at 8s. The optimal block duration is approximately 4-6s for both a constant and varying ISI. Discussion : Since the accuracy of estimating a particular delay generally increases with the square root of the number of samples, the results suggest that 3.5 runs of 192s in duration (at a TR of 1s) are needed in order to accurately detect a latency difference of only 100ms (p<0.05). The choice of the proper stimulus design has a large impact on this, with less optimal designs possibly resulting in 2- 3 times the standard deviation, and therefore requiring many more samples for accurate latency determination. References : 1. A. Dale et al., Hum. Brain Map.8(2-3), 1999. 2. K. Friston et al., NeuroImage 10(5) 1999. 3. R.M. Birn et al, NeuroImage 15, 2002. 4. Z. Saad et al, Hum. Brain Map., 13(2) 2001. 0 10 20 30 0 0.2 0.4 0.6 0.8 Stimulus Block Duration Stimulus Block Duration (s) Std. Dev. A: Standard deviation of latency estimate for varying inter-stimulus intervals, at a stimulus duration of 1s (o) or 4s (+). Lines represent ISI’s constant in time. B: Standard deviation of latency estimate for different stimulus block durations and an equal amount of time in stimulus and control states. Circles: varying ISI, Line: constant block duration and ISI. 0 10 20 30 0 0.2 0.4 0.6 0.8 Inter-Stimulus Interval Average Inter-Stimulus Interval (s) Std. Dev. SD = 1s SD = 4s B A 0 10 20 30 0 0.2 0.4 0.6 0.8 Stimulus Block Duration Stimulus Block Duration (s) Std. Dev. A: Standard deviation of latency estimate for varying inter-stimulus intervals, at a stimulus duration of 1s (o) or 4s (+). Lines represent ISI’s constant in time. B: Standard deviation of latency estimate for different stimulus block durations and an equal amount of time in stimulus and control states. Circles: varying ISI, Line: constant block duration and ISI. 0 10 20 30 0 0.2 0.4 0.6 0.8 Inter-Stimulus Interval Average Inter-Stimulus Interval (s) Std. Dev. SD = 1s SD = 4s 0 10 20 30 0 0.2 0.4 0.6 0.8 Stimulus Block Duration Stimulus Block Duration (s) Std. Dev. 0 10 20 30 0 0.2 0.4 0.6 0.8 Stimulus Block Duration Stimulus Block Duration (s) Std. Dev. A: Standard deviation of latency estimate for varying inter-stimulus intervals, at a stimulus duration of 1s (o) or 4s (+). Lines represent ISI’s constant in time. B: Standard deviation of latency estimate for different stimulus block durations and an equal amount of time in stimulus and control states. Circles: varying ISI, Line: constant block duration and ISI. 0 10 20 30 0 0.2 0.4 0.6 0.8 Inter-Stimulus Interval Average Inter-Stimulus Interval (s) Std. Dev. SD = 1s SD = 4s 0 10 20 30 0 0.2 0.4 0.6 0.8 Inter-Stimulus Interval Average Inter-Stimulus Interval (s) Std. Dev. SD = 1s SD = 4s B A 1784 Proc. Intl. Soc. Mag. Reson. Med. 11 (2003)