It is well recognized that sites of brain activation could escape detection with functional magnetic resonance imaging (fMRI) if the temporal dynamics of activation and the a priori temporal assumptions of the detection technique are poorly matched. Numerous approaches have been proposed attempting to minimize the assumptions concerning activation dynamics in order to avoid the possibility of missed activation [e.g., Andersen et al., 1999
; Brammer, 1998
; Clare et al., 1999
; Golay et al., 1998
]. However, for the most part, these techniques have remained more of theoretical interest than practical significance because there have not been striking examples of their necessity.
The wide range of temporal fMRI responses recently found in human auditory cortex to prolonged (e.g., 30 sec) stimuli provide a clear illustration of the need for methods capable of detecting an extensive range of response waveshapes in “epoch” (i.e., “block”) related fMRI paradigms [Giraud et al., 2000
; Harms and Melcher, 2002
; Seifritz et al., 2002
]. Depending on the time-envelope of a sound stimulus, the temporal dynamics of auditory cortical activation can vary from the sustained waveshapes seen typically in fMRI to atypical “phasic” waveshapes that include prominent peaks just after sound onset and offset (see, e.g., ) [see also Harms, 2002
; Harms and Melcher, 2002
; Harms et al., 2001
]. For instance, 30-sec trains of repeated noise bursts with a low burst repetition rate (e.g., 2/sec) produce highly sustained responses whereas trains with a high rate (e.g., 35/sec) elicit phasic responses in the same cortical areas. The demonstrated capacity of auditory cortex to show these variations in fMRI waveshape raises the possibility of similarly dramatic, but as yet unidentified variations in other cortical areas. It also raises the possibility of additional, as yet undetected modes of response both within and outside the auditory system.
Figure 2 Top three rows: Activation maps obtained using the OSORU, sinusoidal, and sustained-only basis sets, for two different stimuli that elicit sustained (left) or phasic (right) responses. The OSORU and sinusoidal basis sets perform well, regardless of underlying (more ...)
That some forms of activation can be easily missed is clearly illustrated using one of the most statistically powerful, but also the most constrained of detection methods: cross-correlation with an assumed response waveshape. For a commonly used cross-correlating function, a smoothed boxcar, the cross-correlation approach performs well when activation is sustained, but poorly when it is not. This point is well illustrated by the poor detection of phasic responses in auditory cortex, as compared to the good detection of sustained responses (e.g., , bottom activation maps). In cases like auditory cortex, where the extremes of response waveshape are quite different, a detection technique with highly constrained assumptions concerning waveshape is bound to fail at one end of the waveshape spectrum or the other. A method that allows for a wide range of temporal dynamics is, therefore, essential if activation is to be detected reliably. The overall objective of the present study was to develop such a method. We specifically sought an approach that would provide information about the underlying waveshape of activation as an automatic by-product of detection.
Of the various approaches with the potential to detect a range of response waveshapes, we identified the general linear model (GLM) as having, in principle, the characteristics needed to meet our goals, and rejected several other alternatives because they did not satisfy our requirements. In theory, a signal decomposition based on wavelet analysis may support the detection of responses with dynamics that vary over different temporal scales [Brammer, 1998
; von Tscharner and Thulborn, 2001
]. However, a wavelet transformation does not necessarily facilitate the extraction of directly pertinent, interpretable information concerning the temporal dynamics of activation. Other possible alternatives, such as autocorrelation analysis [Paradis et al., 1996
], fuzzy clustering [Baumgartner et al., 1998
; Chuang et al., 1999
; Fadili et al., 2000
; Golay et al., 1998
], and principle component analysis [Andersen et al., 1999
; Sychra et al., 1994
], lack a well-defined statistic that supports inference on a univariate, voxel-by-voxel, basis. The GLM, on the other hand, does not suffer from this limitation and can provide direct information concerning the temporal properties of activation for individual voxels.
The basic idea behind the GLM is that the response can be modeled as a weighted sum of “basis functions.” The amplitudes of the basis functions are estimated so as to give the best overall fit to the measured response. As a by-product of detection under the GLM, the basis functions and their corresponding amplitudes can provide direct information about the underlying temporal responses, provided the basis functions are chosen to relate directly to specific features of the waveshape of activation. Additional strengths of the GLM include: (1) the capability to handle the correlated nature of fMRI time-series, (2) the existence of a well-defined, easily-computed statistic (F-statistic) for estimating significance relative to the null-hypothesis, and (3) good statistical power characteristics [Ardekani and Kanno, 1998
An important element of the present study was devising a flexible, yet concise, set of basis functions for modeling a range of cortical responses within the GLM framework. The vast majority of previous implementations of the GLM have used a single, “sustained” basis function (equivalent to cross-correlation with a smoothed boxcar or, similarly, a t
-test). Some studies have used a two-element basis set, supplementing the standard sustained function with its temporal derivative or a component with an exponential decay [Friston et al., 2000
; Giraud et al., 2000
]. However, this implementation remains limited in terms of the range of response waveshapes that can be handled. The opposite extreme is to use basis functions that lead to a direct estimate of all time-points of the response (i.e., finite impulse response models), thereby allowing for complete flexibility in possible response dynamics (and truly unbiased response estimation) [Burock and Dale, 2000
; Miezin et al., 2000
]. However, such an approach will typically be ill advised for epoch-related paradigms with prolonged stimulus presentation, since the direct estimation of many time-points will result in a statistical test with drastically reduced power relative to a test based on a small, well-chosen basis set.
An example of a small, well-chosen basis set is a series of sinusoids (i.e., a truncated Fourier series) [Ardekani et al., 1999
; Bullmore et al., 1996
; Friston et al., 1995b
]. The GLM using this basis set is generally acknowledged to be powerful in terms of detection, and flexible in that it can handle a wide range of temporal responses. In theory, this approach is capable of detecting any response with frequency components in the range of the basis set. A downside, however, is that sinusoidal basis functions do not necessarily have physiological meaning. Thus, while providing a powerful means for detecting a variety of responses, a sinusoidal basis set does not meet our objective of providing direct information about different response components.
The present study took a different approach from previous GLM work in that the choice of basis functions was neurophysiologically motivated. Specifically, the form of each function was chosen to mirror the general shape of a particular component in actual fMRI responses to prolonged (e.g., 30 sec) stimuli, the idea being that certain components may indicate particular aspects of underlying neural activity (e.g., the prominent peaks after stimulus onset and offset in the phasic responses of auditory cortex likely reflect neural activity in response to stimulus onset and offset) [Harms and Melcher, 2002
]. Thus, the basis functions, together with their amplitudes, should provide direct, readily interpretable information about the temporal dynamics of responses, and hence the neural activity underlying them. A key difference between the present approach and some previous physiologically-driven detection methods [Purdon et al., 2001
] is that our choice of basis functions was oriented toward understanding the neural activity behind fMRI responses, rather than modeling the hemodynamics. Here, five basis functions were chosen. These will be referred to as the “OSORU” basis set, a name that derives from descriptions of the individual components (Onset, Sustained, Offset, Ramp, Undershoot; see ).
The five physiologically-motivated functions of the OSORU basis set. The shaded area indicates the period of sound stimulation.
The present study examined the utility of the OSORU basis set in three ways. First, the detection capability of the OSORU basis set in epoch-related paradigms was assessed by testing whether the extent of detected activation was (1) greater than or equal to the extent obtained using one of the most common detection methods, i.e., comparison with a (smoothed) boxcar reference waveform, and (2) comparable to that obtained using a sinusoidal basis set, an alternative basis set generally acknowledged to be powerful, yet flexible, in terms of response detection. Second, the ability of the OSORU basis set to quantify different waveshape components was assessed by comparing the amplitude of different OSORU basis functions (or combinations thereof) with direct measurements (e.g., baseline to peak amplitudes) from the waveforms themselves. Both the detection and quantification tests were conducted using an extensive and challenging database composed of auditory cortical responses to a variety of sounds. Finally, we examined the utility of the OSORU basis set for extracting physiological information concerning responding brain areas. As an example, we derived one particular measure from the OSORU basis functions that summarizes the degree to which auditory cortex responds to sound in a transient vs. sustained manner. We show that the relative amounts of transient and sustained activity can be captured in this measure, and can be spatially mapped across cortical areas.
Overall, the GLM method using the OSORU basis set provided reliable detection and straightforward characterization of the temporal dynamics of auditory cortical activation. Although developed and tested on the human auditory system, this approach should also be applicable, both in concept and detail, to other brain systems and species.