The use of the time bisection procedure allowed for a detailed analysis of AD patients' timing behavior within the theoretical framework of Scalar Timing Theory, with particular attention devoted to the function of the memory components.
The results presented above indicate that patients diagnosed with probable mild Alzheimer's disease had diminished ability to discriminate intervals in the sub-second range, as shown by the substantially increased WR index in the short time bisection task, with respect to the long time bisection task. The same pattern of results was obtained for elderly participants. Thus, for these two groups, interval timing on different anchor durations was not properly scalar, that is, DL and BP did not co-vary proportionally in the sub- and supra-second time bisection tasks, with AD patients displaying the poorest sensitivity to ms-scale intervals, compared to both young and elderly controls. Furthermore, contrary to the other groups, AD patients generally failed to maintain a constant timing criterion over the same bisected duration, as indicated by the substantial imprecision in making both repeated short and long temporal judgments. In contrast, they did not systematically over- or under-estimate durations relative to control participants (BP for the three groups was comparable in both tasks).
Millisecond and second durations were used in our study to better isolate deficits specific to temporal processing from more generalized cognitive impairments. If timing difficulties of AD patients were mainly due to higher order cognitive impairments, their temporal performance should have been much worse for discrimination of supra-second intervals, that are known to require additional mnemonic and attentional demands to be correctly encoded. The obtained results suggest that this was not the case. Indeed, apart from an overall decreased precision of performance, that may be indicative of an unspecific deficit in sustaining attention throughout both short and long time bisection tasks, AD patients seemed to display more difficulties in timing millisecond durations. To a lesser extent, the same observation holds for the elderly group. Therefore, performance of AD patients and elderly subjects can be interpreted as primarily dependent on mechanisms specifically serving timing operations.
One of the advantages of the SET model is that it is modular, thus allowing to make assumptions about the correlation existing between a certain temporal behavioral pattern and the selective involvement of cognitive stages included in the model.
Studies investigating the effect of selective brain lesions or pharmacological manipulations on time bisection or peak-interval responses in animals have identified characteristic patterns of accuracy (under- or over-estimation) and variability (decreased or increased) of timing behavior that are specifically associated to clock [5, 7, 8] or memory [5, 9–11] disruptions. It is assumed that clock variability is relatively small compared to memory variability, so that changes in clock speed mostly affect accuracy, horizontally displacing psychometric functions. This contrasts with the memory pattern which is represented by both accuracy and variability changes, that respectively modify horizontal position and slope (or shape) of temporal response curves. Furthermore, after the introduction of a variable that varies clock pulse discharge, accuracy is immediately altered, but it then returns to the criterion time as clock can be recalibrated quickly. On the contrary, changes in accuracy and variability induced by variables distorting pulse encoding into memory are gradual and long lasting, as memory-storage speed cannot be rapidly readjusted [26, 27, 45]. It has been additionally suggested that, within the memory pattern, time overestimation denoted by rightward shifts of the psychometric function, might depend on a selective reference memory breakdown following frontal lesions, whereas time underestimation and variability increase, that are mostly subsequent to medio-temporal lesions, might be interpreted as working memory deficits.
It is important to point out that a cautious approach should be adopted when comparing results obtained from animal and human studies. The effects of pharmacological manipulations in animals are generally studied under "state-change" design, where differences between conditions are amplified by the procedure of directly contrasting the behavioral effects produced on the same subject by two different drugs. In contrast, normal or pathological conditions in humans can be described as "steady-state" designs, where the observed behavioral effects are not experimentally produced. Thus, when employing time bisection with human patients, some of the above-mentioned SET predictions about the expected timing behavior should be partly reformulated. In particular, changes in the clock rate should not be evident from patients' bisection accuracy, since bisection point (denoting accuracy) is typically measured after that any hypothetical rescaling of distorted clock speed has occurred. Moreover, as already observed elsewhere , contrary to other tasks requiring a perceptual estimation of an objective duration, in which differences in clock speed are directly reflected by performance differences (e.g., a faster internal clock would correspond to overestimation of the to-be-timed interval), bisection judgments result from a comparison between two intervals (the reference and the test intervals) that have both been encoded according to subjective internal clock speed. Hence, independently of whether clock rate is distorted or not, the location of bisection point should not change significantly. In contrast, if memory or attention processes are influencing temporal performance, psychometric functions are expected to shift. For instance, working and reference memory disruptions may respectively alter the storage of the test and anchor durations, so that bisection responses will be given according to two different subjective time scales, consequently affecting bisection point. Finally, though conceptually very elegant, behavioral patterns predicted by SET through pharmacological manipulations are not so evident when analyzing patients' timing behavior and in practice it is difficult to separate clock from memory variance.
Given these observations, the lack of any significant shift in the bisection function of AD patients in the present study might be referred to different alternative interpretations.
First, a general functional drop extending to both the working and reference memory components due to a severe widespread decreasing cholinergic activity of the BFCS might have been responsible for compensating opposite horizontal shifts in the psychometric curves. In addition, although the patients included in the present study were all diagnosed with the same severity level of AD, the full extent of the pathology cannot be established with certainty in any subject and the degeneration might have differentially involved the regions of the BFCS, leading to the cancellation of specific temporal distortion when analysing the average behavioral performance. Alternatively, a very mild cholinergic dysfunction might have not been sufficiently important to produce any appreciable temporal distortion or to be detected by the time bisection tasks used here.
An impairment of the clock component is also possible, although the decreased temporal sensitivity of AD patients, especially observed in the domain of millisecond intervals, represents a hallmark of memory variance. Increased WR index and consequent violation of the scalar property in the short time bisection task might be indeed selectively due to a reference memory dysfunction, characterized by a greater degree of noise in the memory distributions of millisecond anchor durations (100 and 600 ms), compared to second anchor durations (1 and 3 s). Impaired temporal sensitivity displayed by a group of frontal lobe patients tested with both sub- and supra-second time bisection tasks has been interpreted as the effect of a potential damage at the reference memory system . Further support to this interpretation is given by a number of evidences indicating that the frontal lobes, besides their very well known contribution to working memory, may be particularly crucial to form and manipulate temporal representations in reference memory [8, 18, 19, 41].
On the other hand, a random error at the working memory level might be hypothesized, with AD patients failing to encode the correct number of pulses at the end of each presented millisecond duration, thus significantly increasing timing variability. Patients with resection of right medial-temporal lobe, a brain structure that is strongly implicated in working memory processes, were found to selectively increase DL and WR values when discriminating intervals within a duration range less than 1000 ms . Additional evidence for an involvement of temporal lobe structures in the current behavioral pattern of results comes also from literature attempting to isolate neural systems that are used for timing durations at the sub-second and several second ranges. By means of fMRI, significantly greater activity has been observed in middle and superior temporal gyri during estimation of a 600-ms interval compared to a 3-s interval .
Finally, also a change in the decisional bias at the comparator level during the tasks, that might be related to AD patients' attentional disturbances, would have possibly both flattened bisection curves, as indexed by increased WR values, and increased the proportion of variance unexplained by the logistic model, as evidenced by decreased precision.
Our results are consistent with previous studies [34, 36, 37] showing that AD participants were more variable and imprecise in their time estimations than controls. Moreover, the present findings support the observation that AD can be associated with both under- and over-estimation or with no bias, but always in the framework of variability. For example, Carrasco and coworkers  found that some AD patients overproduced time, whereas others underproduced time, so that, on average, the AD group was not significantly less accurate in timing than the control group.
There is some evidence that timing also changes with age. Some authors have suggested that age-related changes in duration judgments depend on slowing down of the internal clock [46–49], some others have indicated that impaired temporal information processing in older adults may be mainly related to reduced attentional resources [50, 51] or memory deficits [52, 53]. Since in the present study the behavioral pattern of elderly participants (decreased sensitivity to millisecond-scale durations, with respect to young controls) is comparable, though milder, to that of AD patients, we put forward the same alternative hypotheses described above for explaining AD patients' performance.
Finally, it is important to note that the present results are not consistent with some previous findings showing that AD patients are compromised in judging durations in the range of seconds [34, 36, 37]. However, the majority of timing studies in AD have only employed durations in the range of several seconds, without no comparison with millisecond timing performance. Thus, as mentioned previously, it is possible that the timing deficits reported by those studies strongly depended on the additional cognitive resources required to encode longer durations, making difficult to isolate temporal perception dysfunctions from more generalized cognitive impairments.