The timing of tics is fractal, even in the first few months of a tic disorder

What is it about?

More than 20 years ago, Bradley Peterson and James Leckman published results showing that the timing of tics in Tourette syndrome followed a fractal pattern. Let's stop to explain what that means. The timing of repeated events can take several patterns. Clicks from a Geiger counter occur at completely random intervals. There's no way to predict when the next click will happen. At the other extreme is purely rhythmic timing, as in music. In a Haydn song, you usually know when the next note will be sung. No Haydn seek. (Sorry, couldn't resist.) Fractal timing is kind of in between. It has structure, so it's not technically random, but the structure is not simple or perfectly predictable. Specifically, tic timing can show self-similarity at different time scales. A relevant example is shown in Fig. 1A of our publication (https://royalsocietypublishing.org/cms/asset/6e6c34cb-5283-4267-904b-ab6bd3415be2/rsif20210742f01.jpg). Tics tend to cluster into bouts or bursts of tics, but those bursts themselves tend to cluster into clumps of bursts of tics, or as Peterson and Leckman called them, bouts of bouts of tics. Bursts of tics occur over short intervals (like tic-tic-pause-tic-pause-pause-pause-tic-tic-tic-pause-tic-tic-tic-tic over a time frame of, say, 20 seconds). But over the next hour, they also tend to have a pattern of a few minutes when tics are more frequent, followed by several minutes with fewer tics. And similarly, "bad weeks" with frequent tics often interrupt longer periods of relative tic quiescence. Our first goal was simply to replicate the finding of Drs. Peterson and Leckman. We had collected over the past 10 years a large number of tic timing patterns over 5-minute periods in children with Provisional Tic Disorder. They'd had tics for only about 4 months on average. We had additional data from the same children when their tic disorder had its first birthday, which by convention is when Tourette syndrome can be diagnosed. And at both of these occasions, we had timed tics while the child just sat there, again while asked to suppress tics, and again while we essentially paid them not to tic (we gave a small reward for every 10-second block of time with no tics). This work was possible due to analytic methods Drs. Beeler and Chakrabarty have used in other settings to quantify the fractality of tics even over relatively brief time intervals. The measure used was the fractal dimension, Df. Our results showed that tics show fractal timing even when they first develop. Additionally, the fractal dimension Df increases both with tic improvement over time and during successful tic suppression.

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Photo by Andor R on Unsplash

Photo by Andor R on Unsplash

Why is it important?

First of all, we can confirm conclusions that have awaited replication for over 20 years. Second, tics are fractal even when they first develop. Therefore the fractal timing can't be a slow adaptation to living with and adapting to tics over a year or longer. Third, we show that successful intentional tic suppression increases the fractal dimension Df. Fourth, Df can provide an alternative measure of tic severity. Finally, we hypothesize that patients with functional tic-like movements or vocalizations in people without a typical tic disorder will show a very different timing of tics. If true, measuring the fractal dimension of these symptoms may provide an objective "laboratory test" for diagnosing functional tics versus Tourette syndrome. My colleague Keisuke Ueda and I are planning a study to test that hypothesis.

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