Fig 1.
The BG network consists of 4 types of nuclei placed in cubic space with internal connections between each type. These nuclei are connected through excitatory (black lines) and inhibitory (red dashed lines) synopsis. The charge balanced DBS signal is applied at the centric neuron of the STN population and is added with an interphase delay to provide better desynchronization results while activating silent neurons. Th neurons received a pulse train representing the sensory motor cortex input to the BG network. For clarity, only 27 neurons in each subpopulation are shown here, however, the network is able to model large populations as well (1000 neurons in each nucleus).
Table 1.
Nominal values of the BG model parameters.
Fig 2.
The LFP is recorded from the center of the STN population and then filtered with a damped oscillator. The result is shifted through a linear delayed feedback block and is used to adjust the DBS current. The frequency of the biphasic DBS signal is adjusted linearly based on the amplitude of . The larger the amplitude of
is, the higher the frequency of the DBS biphasic pulses will be.
Fig 3.
A) The firing patterns of 4 nuclei were generated by our proposed model under the healthy condition. Th and STN cells showed tonic spikes in presence of sensory motor cortex input, while GPe and GPi cells had continuous and repetitive firings. B) In PD state, Th cells showed abnormal firings such as burst patterns, repetitive spikes for a single stimulus and failure to fire in presence of stimulus pulses. GPe and GPi neurons showed more burst patterns while STN firings remained similar to the healthy condition. C) The average firing rate within 125 neurons of each nuclei were examined for healthy and PD states. From healthy to PD, the STN and GPi firing rates were increased, while the Th and GPe firing rates were decreased. These changes were much compatible with actual recordings [62] compared to previously proposed BG models [60, 63].
Table 2.
Characteristics of neuronal firings.
Fig 4.
The measured LFP and its filtered signal show a rhythmic oscillation due to PD.
Fig 5.
Adjusted stimulation signal by FAS protocol.
The frequency of the DBS signal is modulated based on the feedback control signal (blue line). Peaks of the control signal indicate high synchronization and therefore, HFS DBS is used for maximum therapeutic effects. With lower amplitudes of the control signal, the urge for HFS decreases and IDBS is then adapted to lower frequencies. The cathodic and anodic peaks of the stimulus signal were set to 100 μA and -10 μA, respectively. The control signal is magnified 100 times for better clarification.
Fig 6.
Desynchronization of STN population by various DBS protocols.
A) DBS signals tends to abrupt the synchronization of the STN population, however, closed loop stimulation such as FAS and Pulsatile show better desynchronization effects. B) The normalized PSD of the LFP measurements for healthy, PD and different stimulation methods are shown. The LFP is down sampled and filtered using Welch’s Method and both FAS and Pulsatile were able to suppress the 14 Hz beta band oscillations, while FAS achieved better desynchronization for 34Hz oscillations. The PSD of HFS and VFS shows similar oscillation frequency with the ability to suppress the low beta band oscillations, whereas the VFS method also shows a small oscillation at 9 Hz consistent with the PSD of the healthy condition.
Table 3.
Synchrony measures for different stimulation protocols.
Fig 7.
Closed and open loop protocols in desynchronizing STN neurons.
A) Synchronous behavior observed under PD condition in raster plot (left panel) and spectrogram (right panel). B) The spectrogram of synchronization while FAS was applied was the lowest, indicating the capability of frequency modulated protocols. The mixture of responses in neuronal firings was prevailing in the FAS protocol (left panel). C) The Pulsatile method also achieved great desynchronization results and the neuronal firings were observed to be sparse. Open loop stimulation methods such as HFS and VFS (D and E, respectively) showed semi-synched dynamics in the firing patterns (left panels). Also, the VFS method showed high synchronization at 100 Hz, as it lacks a precise method defining the length of each stimulation block.
Fig 8.
Population size effect on the total energy consumption.
As the network size increases, the EC value for FAS and Pulsatile protocols ascend linearly with a moderate slope. For big networks (>512 neurons in each nucleus), FAS shows to be more energy efficient than the Pulsatile stimulation. The EC for open loop stimulation therapies such as HFS protocol grows almost exponentially as the population gets bigger. VFS was able to show a linear growth in EC as the population size increases, however, it drastically became less energy efficient for medium and big populations (>216 neurons in each nucleus).