Fluctuation refers to the variability or changes over time in a particular measure or phenomenon. In the context of the study you mentioned on deep brain stimulation (DBS) and local field potentials (LFPs) in Parkinson's disease (PD), “fluctuation” describes the variation in neural activity (specifically LFP power) across different behavioral states (e.g., sleep and wakefulness) over time.

### In the Context of the Study:

1. LFP Fluctuations: In this case, LFPs are electrical signals recorded from the subthalamic nucleus (STN) in patients with PD who are undergoing DBS. The fluctuation of LFP power refers to the changes in the amplitude or strength of these signals as the patient transitions between sleep and wakefulness.

2. State-Dependent Fluctuations: The study finds that LFPs fluctuate differently during wakefulness compared to sleep, with LFP power being higher during wakefulness than during sleep. This means that the strength of the electrical oscillations recorded from the STN varies depending on whether the person is awake or asleep. Such fluctuations can be used as markers to differentiate these two states.

3. Diurnal Fluctuations: The term diurnal fluctuations refers to the variations in LFP activity that occur over the course of a day (following the natural sleep-wake cycle). In the study, the fluctuations in LFP power were more strongly correlated during the nighttime, indicating that the sleep-wake cycle has a distinct effect on the oscillatory patterns in the STN.

### Why Is Fluctuation Important in This Context?

- Biological Significance: The fluctuation of LFPs across the sleep-wake cycle is important because it provides insight into how the brain’s neural activity is linked to behavioral states like sleep and wakefulness. In PD, where there is already abnormal neural oscillation, understanding these fluctuations may help improve treatments such as DBS for both motor and non-motor symptoms, like sleep disorders.

- Clinical Implications: The ability to monitor LFP fluctuations could potentially lead to closed-loop DBS systems. These systems would adjust the stimulation parameters in real-time based on fluctuations in brain activity, offering a personalized approach that adapts to the patient’s natural sleep-wake cycle and improves the management of symptoms, such as sleep disturbances, in PD.

In summary, “fluctuation” in this study refers to the variability in the power of LFP signals across different times of day, particularly distinguishing between sleep and wakefulness. This could provide crucial data for refining closed-loop DBS systems and improving care for PD patients with sleep disorders.