### abstract ###
Cortico-basal ganglia-thalamocortical circuits are severely disrupted by the dopamine depletion of Parkinson's disease, leading to pathologically exaggerated beta oscillations.
Abnormal rhythms, found in several circuit nodes are correlated with movement impairments but their neural basis remains unclear.
Here, we used dynamic causal modelling and the 6-hydroxydopamine-lesioned rat model of PD to examine the effective connectivity underlying these spectral abnormalities.
We acquired auto-spectral and cross-spectral measures of beta oscillations from local field potential recordings made simultaneously in the frontal cortex, striatum, external globus pallidus and subthalamic nucleus, and used these data to optimise neurobiologically plausible models.
Chronic dopamine depletion reorganised the cortico-basal ganglia-thalamocortical circuit, with increased effective connectivity in the pathway from cortex to STN and decreased connectivity from STN to GPe.
Moreover, a contribution analysis of the Parkinsonian circuit distinguished between pathogenic and compensatory processes and revealed how effective connectivity along the indirect pathway acquired a strategic importance that underpins beta oscillations.
In modelling excessive beta synchrony in PD, these findings provide a novel perspective on how altered connectivity in basal ganglia-thalamocortical circuits reflects a balance between pathogenesis and compensation, and predicts potential new therapeutic targets to overcome dysfunctional oscillations.
### introduction ###
In Parkinson's disease, degeneration of midbrain dopamine neurons severely disrupts neuronal activity in looping circuits formed by cortico-basal ganglia -thalamocortical connections . Studies have shown that excessive oscillations at beta frequencies are a key pathophysiological feature of these Parkinsonian circuits, when recorded at the level of unit activity and/or local field potentials in several key circuit nodes.
These nodes include the frontal cortex, subthalamic nucleus, external globus pallidus and internal globus pallidus . Suppression of pathological beta-activity is achieved by dopamine replacement therapies  and surgical treatments e.g. high-frequency, deep brain stimulation of the STN; where prolonged attenuation after stimulation is observed . Bradykinesia and rigidity are the primary motor impairments associated with beta activity and, following dopamine replacement therapies, improvements in these motor deficits correlate with reductions in beta power . Moreover, a recent report has shown that stimulating the STN at beta frequencies exacerbates motor impairments in Parkinsonian rodents , in line with similar findings in PD patients .
Precisely how dopamine depletion leads to abnormal beta power is unknown.
Recent work in rodents has revealed that excessive beta-activity emerges in cortex and STN after chronic dopamine loss but not after acute dopamine receptor blockade . Here, we examine whether changes in effective connectivity between the nodes of the cortico-basal ganglia-thalamocortical network can account for enhanced beta oscillations following chronic dopamine loss.
To test this hypothesis we used dynamic causal modelling.
This approach allows one to characterise the distributed neuronal architectures underlying spectral activity in LFPs.
DCM is a framework for fitting differential equations to brain imaging data and making inferences about parameters and models using a Bayesian approach.
A range of differential equation models have been developed for various imaging modalities and output data features.
The current library of DCMs includes DCM for fMRI, DCM for event related potentials and DCM for steady state responses.
The current paper is based on DCM-SSR, designed to fit spectral data features .
Using spectral data, recorded simultaneously from multiple basal ganglia nuclei and the somatic sensory-motor cortex, we asked whether systematic changes in re-entrant neural circuits produce the excessive beta oscillations observed in LFPs recorded from the 6-hydroxydopamine -lesioned rat model of PD . We inverted the models using LFP data collected simultaneously from electrodes implanted in frontal cortex, striatum, GPe and STN.
Specifically, we used neural mass models that characterise the main projection cell types at each circuit node as glutamatergic or GABAergic.
Neural mass models describe neuronal dynamics in terms of the average neurophysiological states over populations of neurons.
Inference on effective connectivity differences observed between the Parkinsonian and control cases was based on a posteriori estimates of connectivity and synaptic parameters.
Using these estimates, we characterised the sensitivity of beta oscillations to changes in particular connection strengths to identify candidate connections that may represent therapeutic targets in idiopathic PD.
Measures of functional connectivity have been applied previously to examine frequency-specific signal correlations between nodes in the cortico-basal ganglia-thalamocortical network.
These measures have highlighted excessive coupling between the cortex and STN  and between STN and GPe  in animal models of PD. While functional connectivity and effective connectivity measures share some technical aspects e.g. likelihood models  or Bayesian estimators , the underlying concepts are fundamentally different . The distinction between functional connectivity and effective connectivity emerged from the analysis of electrophysiological time series: Aertsen et al. , used the term effective connectivity to define the neuronal interactions that could explain observed spike trains using a minimum simple neuronal model.
In what follows, we employ such a minimum model approach, using the key elements of known cortico-basal-ganglia-thalamocortical interactions.
Our model predicts the output of this loop circuit in vivo, where we assume observed responses are caused by interactions among neuronal populations or sources, with known neurotransmitters and directed connections.
The starting point for analyses of effective connectivity in this paper is the end point of classical functional connectivity analyses; namely, observed cross-spectral densities.
In other words, we place special emphasis on explaining how functional connectivity emerges in terms of directed connections that rest on a particular model of neuronal interactions.
In what follows, we illustrate this approach when applied to the directed circuitry of a cortico-basal ganglia-thalamocortical system.
