Increased motor activity is a defining characteristic of patients with attention-deficit/hyperactivity disorder (ADHD), combined and hyperactive subgroups. This is based on observations of children with ADHD and on objective registrations with actigraphs [1]. Studies of reaction times, as well as other behavioral measures in patients with ADHD, have repeatedly shown increased intraindividual variability (IIV) as a characteristic feature of ADHD [2–18].

Spontaneously hypertensive (SHR/NCrl) rats have been suggested to be an animal model of ADHD [19], and in several test paradigms display behavior similar to that seen in patients with ADHD, including increased motor activity, impulsivity, and inattention. Another similar feature observed in the behavior of SHR/NCrl is increased IIV [20–24]. However, there are divergent views on SHR/NCrl as a valid model of ADHD [25] which may possibly be related to the control strain used in the experiments [26].

A characteristic feature of different disorders or disease processes may be increased order and regularity of behavior, i.e. reduced complexity [27, 28]. Biological systems can seldom be fully characterized by simple linear processes, and additional mathematical methods are required obtained from the field of non-linear system, complexity theory and chaos theory [29]. At a molar, aggregated level, behavioral variability is quantitatively described by measures such as standard deviation and root mean square of successive differences. However, such measures do not capture behavior variability at a local, molecular, moment-to-moment level [30]. Therefore, non-linear methods, such as different measures of complexity and entropy, have in recent years been employed to analyze biological time series. Such methods may give additional information to that obtained by traditional linear methods, and can be used to identify the underlying neural mechanisms of the system being studied.

In the present report, we have analyzed video-recorded motor behavior of SHR/NCrl rats in order to look for differences in behavioral organization between this strain and control rats of the WKY/NHsd strain. In addition to total activity levels and velocity of movement, we have used both linear and non-linear methods to analyze movement patterns. We have used standard deviation (SD) and root mean square successive differences (RMSSD) to indicate the molar, overall level of variability. These measures have been used in the study of reaction time variability in ADHD patients [31] and also in the study of motor activity of psychiatric patients assessed with actigraphs [32–34]. For analyses of molecular behavioral variability, we included analyses of autocorrelations, which have been used to assess response variability in children with ADHD [2, 3]. Additionally, to investigate variability in different frequency domains, we have employed Fourier analyses, which is a well-established method in many different fields, and which have been used together with SD and RMSSD in studies of motor activity [32–34]. To obtain a measure of complexity we have used sample entropy and symbolic dynamics which are two methods that tolerate a reasonable degree of noise (as usually is the case with biological systems). Both methods were used in the actigraph-studies mentioned above [32–34] and also in the study of reaction time variability in ADHD patients where increased variability and reduced complexity were found [31].

Reduced behavioral complexity is suggested to be a characteristic of different disorders or disease processes, and several studies show that intraindividual variability is increased in ADHD as well as in SHR/NCrl. Thus, our hypothesis when conducting this study was that the behavior of SHR/NCrl rats would be characterized by increased variability and reduced complexity compared to WKY/NHsd rats, both with regard to total activity and velocity of movement.

The present study examined organization of video-recorded motor behavior in SHR/NCrl and WKY/NHsd controls using linear and non-linear methods. The main finding of the present study is that the motor activity of SHR/NCrl rats is different from WKY/NHsd rats in a number of ways, not only at the level of activity. The SHR/NCrl rats display increased mean and maximum velocity of their movements in addition to a pronounced increased total activity level. Concurrently, the organization of behavior is different in SHR/NCrl and WKY/NHsd controls. At a molar level of analysis, the variability of the time series, the SD and RMSSD, is markedly lower in SHR/NCrl compared to the WKY/NHsd rats when these measures are expressed as percent of the mean. At a molecular level of analysis, in contrast, the Fourier analysis shows that in the SHR/NCrl rats there is an increased variance in the high frequency part of the spectrum, corresponding to a time period of 9–17 s. When analyzing the time series with symbolic dynamics, the SHR/NCrl rats appear to have a higher behavioral complexity, particularly with regard to the total activity level. Similarly, using sample entropy, the complexity of the time series of total activity is higher in the SHR/NCrl rats than in the WKY/NHsd rats, and the lower autocorrelations of velocity in SHR/NCrl than in WKY/NHsd controls show that behavior is less systematic and less predictable from one occurrence to the next in the SHR/NCrl.

The increased total activity level of SHR/NCrl rats compared to the WKY/NHsd strain is in accordance with previous studies and in agreement with SHR/NCrl rats as a model of ADHD [20–24, 44, 45]. Increased activity is a defining feature of ADHD and has been confirmed using objective registrations of motor activity in patients [1, 46].

In SHR/NCrl, increased IIV has been found across a variety of behaviors including maze performance, lever pressing and nose poking [20–24, 44, 45]. The markedly reduced molar IIV in SHR/NCrl, as measured with SD and RMSSD, found in the present study is therefore at first glance surprising and inconsistent with the findings of Perry et al. [24] who used an identical experimental procedure to the one used in the present study, where total test-time was divided into 5 segments, and IIV for operant lever-pressing was expressed as the absolute difference between behavior in each segment and the total test-time mean. One important difference between the studies is that Perry et al. analyzed reinforcer-controlled lever pressing only, whereas the video-recorded behavior analyzed in the present study included reinforcer-controlled movements (lever approach, presses, tray visits, and reinforcer consummation) as well as other movements not controlled by the scheduled reinforcers (e.g. grooming, exploration and motor control). The impact of each of these processes on the observed changes in IIV in SHR/NCrl cannot be disentangled in the present study, but may have contributed to the inconsistent findings. A second important difference between the two studies is that Perry et al. used variability measures corrected for mean whereas SD and RMSSD mean corrections were used in the present study. Although uncorrected SDs and RMSSDs in the present study were higher in SHR/NCrl than in controls for total activity, the means were also much higher in SHR/NCrl than in controls. Thus, the mean-corrections produced lower SDs and RMSSDs in SHR/NCrl than in controls, and it has been argued that this procedure may be overly conservative and overcorrect for SHR/NCrl phenotype [24]. In the analysis of mean velocity, uncorrected SDs and RMSSDs were also higher in SHR/NCrl than in controls, but the differences were smaller, whereas uncorrected SDs and RMSSDs for maximum velocity were lower in SHR/NCrl than in controls. Comparing total activity, mean and maximum velocity using uncorrected SD and RMSSD would therefore give inconsistent results, while correcting for mean gives a consistent picture, with lower SD and RMSSD for SHR/NCrl compared to controls in the range of 51–69%.

Mean corrections have been discussed within the ADHD literature for measures of reaction time (RT) and reaction time variability. In these studies, intraindividual variability has commonly been measured as the standard deviation of RTs without mean correction. Studies have shown that although correlated, RT mean and RT standard deviation have independent components of variance [47]. Additionally, increased mean RT and RT variability may have shared etiology in ADHD [48]. Thus, by correcting for mean, there is a risk of controlling for what one intends to study [49].

The question of dependence between the mean and measures of variability is highly relevant in the present study because the increased mean activity level and variability measures in SHR/NCrl could be expressions of one underlying factor. When looking at data from both rat strains, there are strong correlations between the variability measures and mean values for motor activity, velocity and maximum velocity, and these correlations parallel the differences in variability measures between the strains. However, when examining each strain separately there are fewer correlations and the pattern is clearly different for the two strains. We think this shows that the differences seen between the two strains do not simply reflect differences in total motor activity or velocity of movement, and that studying variability measures give added information concerning the organization of motor activity.

Overall, the analyses of video-recorded behavior during the operant task suggest that behavior is organized differently in SHR/NCrl as compared to WKY/NHsd controls: At a molar level, SHR/NCrl behavior is less variable whereas behavior at a molecular level is more complex than in controls. Increased molecular behavioral complexity in SHR/NCrl compared to WKY/NHsd was found in the Fourier analyses for both mean velocity and maximum velocity of movement, and is consistent with the symbolic dynamics analyses, and the autocorrelations analyses for velocity of movement.

Studying movement patterns, Paulus et al. [50] found differences between Fischer, Lewis, and Sprague–Dawley rats using a spatial scaling exponent quantifying the degree of linear movement versus movement within a circumscribed area (low versus high scaling exponent, respectively), that may in some respect resemble the complexity test we have used. They suggested that a lower scaling exponent in Sprague–Dawley rats compared to Fischer and Lewis rats was related to differences in central serotonergic systems. In a study of SHR and WKY rats, Li and Huang [51] found that the scaling exponent was higher in SHR rats, in accordance with our finding of a higher complexity of total motor activity in these rats. Previous studies have shown a range of neurological changes in SHR. We are in our study unable to separate the possible role of dopaminergic and serotonergic systems in the regulation of movement patterns, and there are differences between SHR and WKY rats in both these systems. Additionally, changes in noradrenergic, glutaminergic neurotransmission and several other systems have been shown in SHR [19, 26, 52–55].

The present finding may partly reflect basic motor processes and point to important differences in the neuronal organization of basic motor activity in SHR/NCrl compared to WKY/NHsd rats. This may indicate similar differences in motor activity regulation in patients with ADHD vs. controls. In a study of reaction times during the CPT-II test, higher variability (using SD and RMSSD) was found in adult ADHD patients compared to clinical controls, but at the same time lower complexity as measured with sample entropy and symbolic dynamic analysis was found in the ADHD group [31]. This finding, an inverse relation between measures of variability and complexity, mirrors the relation between the same measures in the present study. We have seen this same inverse relationship also in a study of motor activity in depressed and schizophrenic patients [32].

Reduced complexity of physiological systems has been postulated to be associated with disease and aging [28], but this may depend on the dynamics of the system under study. Vaillancourt and Newell [56] have suggested that in systems with intrinsic oscillations the opposite may occur, namely that disease processes are accompanied by increased complexity. This has been found in the motor activity of schizophrenic patients [32], and the present findings may fit the same pattern.

Another way to conceptualize the present findings on intraindividual variability is to compare them with human studies showing that variability patterns are different when comparing measures of brain function and behavior. Garrett et al. [57] found in an imaging study that blood oxygen level-dependent signal variability (brain variability) was lower in older compared to younger persons, while reaction time speed variability on different cognitive tasks was higher. Similarly, McIntosh et al. [58] found, when comparing children and young adults, that maturation was accompanied by increased variability of EEG-signals and reduced variability of response times on a facial recognition task.

Studies of behavioral variability in ADHD have produced a complex set of findings. Studying children with ADHD using autocorrelations, predictability of responses was found to be lower in ADHD (i.e. responding was more variable), consistent with the current findings [2]. Additionally, the autocorrelations in ADHD were found to be sensitive to the reinforcement contingencies [3], which has also been found for response time variability [59]. In a study of reaction times in children with ADHD, Castellanos et al. [6] found evidence of multisecond oscillations, with a cycle length of approximately 20 s, and they suggested that this might be due to deficiencies in dopaminergic regulations in the patients. This is intriguingly similar to the findings with Fourier analysis in the present study. Using Fourier analyses, Karalunas et al. found more low-frequency variability and higher faster-frequency variability in ADHD, with non-significant differences between frequency bands [60]. In a study of children with ADHD, Wood et al. [46] found, in addition to increased motor activity, also increased intraindividual variability of the intensity of movements. On the other hand [61], a study of adult ADHD patients found that the patients had both increased activity levels and reduced daytime variability patterns compared to controls. In another study in adults, ADHD patients did not show increased activity levels compared to controls, and variability measures (SD and RMSSD) were not altered, but Fourier analyses revealed higher power in the high frequency range, corresponding to the period from 2 to 8 min [31].

Several mechanisms underlying the increased IIV observed in ADHD have been proposed, including deficient astrocyte energy supply to active neurons, state regulation and working memory problems, arousal-attention regulation, and altered learning processes (see [11, 49] for reviews of etiological models of reaction time variability). The complexity of findings is a challenge to current theories of IIV in ADHD, and obviously underscore the need for further studies that compare measures used to characterize variability, examine possible discrepancies between molar and molecular analyses of variability, and explore variability patterns in both patients and animal models.

The current findings add to this complexity by suggesting the presence of both increased molecular as well as decreased molar behavioral variability in SHR. If valid for ADHD, this finding is a new and interesting contribution to the research on IIV, and suggests that IIV in ADHD is not unitary and explained by one common principle, but may have several underlying mechanism depending on the task used and the behavior analyzed, and may be changed in opposite directions depending on the variability measures used.

There are some important limitations to the present study that must be considered. First, it is not clear what the video-recorded behavior during the operant task reflect (i.e. reinforcer-effects, grooming, exploration, basic motor organization, or other processes) or how the behavioral changes relate to underlying mechanisms. Nevertheless, several changes in IIV in SHR/NCrl were found suggesting that analyses of video-recorded behavior may be a valuable supplement to traditional behavioral measures used in studies of IIV. Second, the decreased molar IIV found in SHR/NCrl relative to controls is based on analyses of SD and RMSSD correcting for mean. However, the use of mean correction has been debated in the ADHD literature, and has been argued to overcorrect for phenotype in studies of SHR/NCrl [24]. The present analyses using mean corrections produced more consistent results, with variability changes in opposite directions, compared to analyses using mean corrections, underscoring the importance of mean corrections in analyses of variability.

This study shows that SHR/NCrl rats, a postulated animal model of ADHD, are different form WKY/NHsd rats in a number of measures related to motor activity. In addition to increased activity levels, the most pronounced findings are increased mean and maximum velocity of movements, and reduced variability for all these measures when assessed with SD and RMSSD corrected for mean. There is also an increased complexity of movement patterns in the SHR/NCrl rats. These results point to differences in the neuronal organization of movements that may be related to the known differences in neurotransmitter systems between these two rat strains. Even though these findings have no immediate implications for the diagnosis or treatment of ADHD patients, they may be used to explore further the mechanisms of motor activity regulation in general, and alterations in neurodevelopmental disorders such as ADHD.