Multiple-time-scale framework for understanding the progression of Parkinson's disease

Abstract

Parkinson's disease is marked by neurodegenerative processes that affect the pattern of discharge of basal ganglia neurons. The main features observed in the parkinsonian globus pallidus pars interna (GPi), a subdomain of the basal ganglia that is involved in the regulation of voluntary movement, are pathologically increased and synchronized neuronal activity. How these changes affect the implemented neuronal code is not well understood. Our experimental temporal structure-function analysis shows that in parkinsonian animals the rate-coding window of GPi neurons needed for the proper performance of voluntary actions is reduced. The model of the GPi network that we develop and discuss here reveals indeed that the size of the rate-coding window shrinks as the network activity increases and is expanded if the coupling strength among the neurons is increased. This leads to the novel interpretation that the pathological neuronal synchronization in Parkinson's disease in the GPi is the result of a collective attempt to counterbalance the shrinking of the rate-coding window due to increased activity in GPi neurons.

On the motion of spikes: a model of multifractality as observed in the neuronal activity of the human basal ganglia

“…In particular, several authors offered evidence of complex time patterns in the neuronal activity of the basal ganglia (see for example the discussion in (Nambu 2005)). In previous work I analyzed first order structure functions (G = 1) of simulated, animal, and human spike trains, and hypothesized that time patterns and rate-coding properties coexist in the basal ganglia (Andres, Gomez et al 2014, Andres, Cerquetti et al 2015, Andres, Cerquetti et al 2016. Here I continue the study to higher orders (G > 1) and show that the scaling behavior of structure functions can be used to obtain the multifractal spectrum of the human, parkinsonian basal ganglia.…”

“…However, the role of these so called passive electric properties of neuronal activity is rarely considered in neurophysiology studies, which usually focus on spiking activity. Previous modeling work on the basal ganglia by our group has shown that a diffusion coefficient might be a critical parameter for the control of information transmission and information deterioration in the parkinsonian GPi [31]. The model introduced here shows that: 1. multifractality of neuronal spike trains depends on diffusive properties, and 2. multifractality of temporal activity is reflected on the spatial domain.…”

“…Here, a nonlinear differential equation is introduced that considers )(*, ,) as a combination of a nonlinear gradient term and a diffusive term. This is relevant to Parkinson's disease, where it has been hypothesized that increased diffusion plays a critical role in the deterioration of information transmission (Andres, Gomez et al 2014). In this context, a progression of Parkinson's disease would be toward higher diffusion coefficients, lowering the velocity of spikes and homogenizing the velocity field.…”

“…These complex structures are mirrored from time into space: a multifractal spectrum is observed in both the temporal and the spatial domains. In previous work I pointed out that there are mathematical similarities between the neuronal activity of the parkinsonian basal ganglia and turbulence , Andres, Gomez et al 2014. Now I introduce a neural field model inspired by Burgers' equation, a well-known equation in the field of fluid dynamics.…”

“…In particular, several authors offered evidence of complex time patterns in the neuronal activity of the basal ganglia (see for example the discussion in [54]). In previous work, we analyzed first order structure functions (B 1) of simulated, animal, and human spike trains, and hypothesized that time patterns and rate-coding properties co-exist in the basal ganglia [25,26,31,55]. Since structure functions of order higher than 1 (B > 1) not only allow to characterize the fractal properties of a signal, but have proven useful for the analysis of human neuronal recordings, to continue their study to higher orders was natural.…”