Exponential state transition dynamics in the rest–activity architecture of patients with bipolar disorder

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Our goal was to model the temporal dynamics of sleep–wake transitions, represented by transitions between rest and activity obtained from actigraphic data, in patients with bipolar disorder using a probabilistic state transition approach.


We collected actigraphic data for 14 days from 20 euthymic patients with bipolar disorder, who had been characterized clinically, demographically, and with respect to their circadian preferences (chronotype). We processed each activity record to generate a series of transitions in both directions between the states of rest (R) and activity (A) and plotted the estimated transition probabilities (pRA and pAR). Each 24-hour period was also divided into a rest phase consisting of the eight consecutive least active hours in each day and an active phase consisting of the 16 consecutive most active hours in each day. We then calculated separate transition probabilities for each of these phases for each participant. We subsequently modeled the rest phase data to find the best fit for rest–activity transitions using maximum likelihood estimation. We also examined the association of transition probabilities with clinical and demographic variables.


The best-fit model for rest–activity transitions during the rest phase was a mixture (bimodal) of exponential functions. Of those patients with rapid cycling, 75% had an evening-type chronotype. Patients with bipolar II disorder taking antidepressants had a lower probability of transitioning back to rest than those not on antidepressants [mean ± SD = 0.050 ± 0.006 versus 0.141 ± 0.058, F(1,15) = 3.40, p < 0.05].


The dynamics of transitions between rest and activity in bipolar disorder can be accounted for by a mixture (bimodal) of exponential functions. Patients taking antidepressants had a reduced probability of sustaining and returning to sleep.

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