Fig 1.
Schematics of the corticothalamic-basal ganglia system.
Subscripts used to denote various neural populations are parenthesized. Arrowed lines denote neural connections and corresponding neurotransmitters, glutamate, GABA, dopamine, and acetylcholine (ACh). The population abbreviations are discussed in the Materials and Methods section. Red arrows highlight three key pathways through the basal ganglia.
Table 1.
Nominal parkinsonian parameters adapted from [63].
Fig 2.
Effects of external pulse train stimulus on population activity.
(a) An example evoked response time series for an external pulse frequency fstim = 130 Hz, pulse width twidth = 130 ms, and coupling strength νax = 10 mV s. (b) Impulse response for a unit input at t = 0 with decay and rise rate parameters, β = 200 s−1 and α = 50 s−1, respectively. (c) Evoked response potential of a given population to the external stimulus represented by the convolution of the impulse response with the stimulus time series. (d) The mean effect of a voltage perturbation evoked by an external stimulus on the distribution of firing rates with a population. Example parameters used are Qmax = 500 s−1, σ′ = 3.3 mm, and θa = 10 mV.
Fig 3.
Parkinsonian activity in the STN.
(a) Power spectrum of STN firing rate ϕζ for mVs. (b) Power spectrum of STN firing rate ϕζ for
mVs.
Fig 4.
Suppression of parkinsonian beta activity for a 150 Hz external stimulus applied at t = 30 s with νζx = −1.2 mVs and mVs.
(a) Time series of STN firing rate ϕζ with DBS stimulus applied at t = 30 s. (b) Power spectrum of STN firing rate ϕζ before DBS application using the time window t = 10–30 s (solid), and during DBS application using a time window t = 30–50 s (dashed).
Fig 5.
Peak power of STN firing rate ϕζ during a 40 s simulation within the frequency band f = 20–30 Hz using a time window t = 20–40 s.
(a) Dependence of peak f = 20–30 Hz power on DBS pulse frequency with νζx = −1.2 mVs and mVs. (b) Change in peak f = 20–30 Hz power by a direct constant perturbation to the soma potential (dashed) and by an indirect perturbation resulting from an oscillating DBS input (solid), as described in Fig 2. For each point Vζ = Vζ + ΔV,
, and
.
Fig 6.
Perturbation of key CTBG loop gains during DBS with νζx = −1.2 mVs, mVs, and all other parameters as defined in Table 1.
(a) Dependence of loop gains on the DBS pulse frequency. (b) Dependence of loop gains on the DBS pulse frequency.
Fig 7.
Power spectrum of parkinsonian STN activity as a function of DBS pulse frequency.
A simulation of 40 s is used with νζx = −1.2 mVs and mVs and a power spectrum of the STN firing rate is calculated over the time window t = 20–40 s.
Fig 8.
Power spectrum of parkinsonian STN activity as a function of DBS pulse frequency with fstim = 24–28 Hz.
A simulation of 40 s is used with νζx = −1.2 mVs and mVs and the power spectrum of the STN firing rate is calculated over the time window t = 20–40 s.