## Hyf

sk+1

FIGURE 19.1 Process model of synchronization (see Vorberg and Schulze, 2002; Vorberg and Wing, 1996). Lowercase variables indicate time points of events, uppercase variables indicate the length of the intervals between events, and subscripted variables are conceptualized as random variables.* An external pacing signal occurs with period P at the time points sk. An internal clock is emitting signals to the motor system at times tk. In absence of error correction, the clock produces timing signals separated by the clock intervals Tk. The motor implementation process produces the kth taps at time rk by adding a random motor delay Mk to the time of the internal timing signal. The real synchronization error Ak between the tap and the pacing signal is perceived (A'k) by a comparator system. The perceived asynchrony is influenced by the perceptual delays, with which the comparator perceives the occurrences of the tap (Fk) and the pacing signal (Sk). The perceived asynchrony is then used to correct the next timing signal with a gain of a, the error correction parameter.

* For purposes of parameter estimation, we consider the perceptual delays F and S to be constants. Schulze and Vorberg (2002) showed that if F and S are regarded as random variables, the variance attached to these delays would inflate the variance estimations of motor delays. However, the main stationary characteristics of the model remain equivalent to the simplified model used here.

uses information about the asynchrony between the action and the external event to adjust the time of the next central command, thus compensating for this discrepancy. The simplest and normative method is a first-order linear correction, in which some fraction, a, of this synchronization error is used to adjust the interval before the next tap. Random errors are rapidly corrected when a is large, although the system would be overcompensating should a be greater than 1. Under some conditions, the adjustment process may take into account more than just the last asynchrony. In such cases, second-order error correction models are more appropriate. Futhermore, error correction may not always be linear (see Pressing, 1999).

Because the "real" asynchrony Ak is not readily available, the phase correction process has to estimate the time of occurrence of the metronome signals and the time of occurrence of the tap (Aschersleben and Prinz, 1995). For the time of the tap, proprioceptive reafferences from the action and the perceived consequences of the action, such as an audible click produced by the response key or the sound of the finger striking the table surface, could suffice. However, even without tactile, proprioceptive, visual, or auditory feedback, stable synchronization between actions and an auditory pacing signal can be accomplished. Billon et al. (1996) examined synchronization in a patient with a severe sensory neuropathy that rendered him functionally deafferented. This patient could maintain a stable phase relationship and correct for perturbations in a relatively normal manner. Thus, the estimate of the time at which an action occurs may also include the copy of the efferent signals (Haggard et al., 2002).

Alternative models have been proposed in which the clock is reset on every trial by a combination of the perceived tap and metronome signal, rather than through a modification process based on the perceived asynchrony (e.g., Hary and Moore, 1987). However, the former model has the advantage of capturing many characteristics of human performance in a parsimonious way (Mates, 1994b) and is more readily consistent with widespread evidence of tempo constancy in musical contexts. For example, humans tend to precede the pacing signal with the action by a constant amount of approximately 50 msec (Dunlap, 1910; Fraisse and Voillaume, 1971). From the framework of the model outlined in Figure 19.1, the phase lead of the taps over the metronome signals can be accounted for by longer delays in the perception of the action than in the perception of the pacing signal. This would lead to a perceived asynchrony that is close to zero, even though the actual asynchrony is negative (Aschersleben and Prinz, 1995; Fraisse, 1980).

19.3.2 Neural Structures Underlying Synchronization and Timing

In the context of this chapter, two neuroimaging papers are of special interest (Jancke et al., 2000; Rao et al., 1997) since they included a synchronization phase and a continuation phase during repetitive tapping. Both studies observed activation in the right anterior cerebellum (hemisphere of lobules I to VI, HI-VI) during the two phases, with the degree of activation approximately equal. A second cerebellar focus in the right inferior lateral hemisphere (H VIII to IX) was reported by Janke et al. (2000) when the participants were paced by an auditory metronome. These authors failed to observe any activation in the basal ganglia. In contrast, Rao et al. (1997) reported significant activation in the putamen during the continuation phase only. Cortical areas were identified in both studies, especially during the synchronization phase, although these tended to be modality specific (e.g., primary or secondary auditory or visual regions).

Unfortunately, the design of these studies makes it difficult to draw strong conclusions. Rao et al. (1997) argue that neural correlates of an internal timing mechanism should be most activated during the continuation phase. Based on this, they argue that their results are consistent with a basal ganglia locus for timing and propose that the cerebellar activation reflects general contributions of this structure to sensorimotor control, consistent with the idea that the movements are similar during synchronization and continuation.

The assumption that internal timing is most pronounced during the continuation phase is suspect. All models of synchronization assume that the internal clock is engaged during paced and unpaced tapping. Indeed, it is difficult to see how participants would tap in advance of the metronome signals if they were not engaging in anticipatory timing. Mates et al. (1994) have shown that such anticipatory behavior holds for intervals up to around 2 sec (see also Fortin, this volume; Fortin and Couture, 2002). Beyond this duration, tapping becomes reactive, following rather than anticipating the tones.

If the demands on an internal timer are similar during the synchronization and continuation phases, then the cerebellar activation profile matches that expected of an internal timing process. However, this finding provides only weak support for a timing interpretation. As noted above, similar activation during both phases would also be expected of areas associated with the planning and execution of the finger movements, independent of whether these movements require the operation of an internal timing system. In sum, the cerebellar activation pattern during repetitive tapping is consistent with what would be expected if neural activity within this structure was involved in determining when each response should be produced, whereas activation within the basal ganglia is not consistent with a timing account. But the cerebellar activity could also be accounted for by hypotheses that do not involve internal timing.

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