Deep brain microelectrode signal: $q$-statistical approach

Abstract: We characterize the amplitude statistics of intraoperative microelectrode recordings (MERs) obtained during deep brain stimulation (DBS) surgery in 46 patients with Parkinson's disease, using 184 recordings equally balanced between inside and outside the subthalamic nucleus (STN). The probability density of every recording is quantitatively well described by a $q$-Gaussian (grounded on a nonadditive entropic functional), $ρ(x) \propto [1 + β(q-1) x^2]^{-1/(q-1)}$, with $q > 1$ in all cases, reflecting persistent long-range temporal correlations inconsistent with Gaussian dynamics. Within the superstatistics framework, the slowly fluctuating local variance visible in the raw MER signals is a physical mechanism that directly generates the $q > 1$ form. Beyond individual fits, $q$ and $β$ collapse across all 184 recordings onto the single functional constraint $q = 3 - 1.85\,β^{-0.33}$ ($R \approx -0.91$), a reduction to one effective degree of freedom that is the quantitative hallmark of near-critical dynamics, previously identified in scale-free network growth and in acoustic precursors of material fracture. The index $q$ is statistically indistinguishable across the STN boundary ($\langle\bar{q}\text{out}/\bar{q}\text{in} \rangle = 1.03$), while the inverse-widthparameter shows a modest systematic difference ($\langle\barβ\text{out}/\barβ\text{in} \rangle = 1.18$). Since $q > 1$ is expected for any brain structure exhibiting long-range correlations, healthy or pathological, it is the tight $q(β)$ coupling, not $q > 1$ per se, that constitutes the candidate near-criticality signature of the parkinsonian cortico-basal-ganglia-thalamocortical loop.