Mean-field modeling of the basal ganglia-thalamocortical system. II: Dynamics of parkinsonian oscillations

Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker intracortical connections in parkinsonian patients. Strict separation of the direct and indirect pathways is not necessary to obtain these results.     

Mean-field modeling of the basal ganglia-thalamocortical system. I: Firing rates in healthy and parkinsonian states

Parkinsonism leads to various electrophysiological changes in the basal ganglia-thalamocortical system (BGTCS), often including elevated discharge rates of the subthalamic nucleus (STN) and the output nuclei, and reduced activity of the globus pallidus external (GPe) segment. These rate changes have been explained qualitatively in terms of the direct/indirect pathway model, involving projections of distinct striatal populations to the output nuclei and GPe. Although these populations partly overlap, evidence suggests dopamine depletion differentially affects cortico-striato-pallidal connection strengths to the two pallidal segments. Dopamine loss may also decrease the striatal signal-to-noise ratio, reducing both corticostriatal coupling and striatal firing thresholds. Additionally, nigrostriatal degeneration may cause secondary changes including weakened lateral inhibition in the GPe, and mesocortical dopamine loss may decrease intracortical excitation and especially inhibition. Here a mean-field model of the BGTCS is presented with structure and parameter estimates closely based on physiology and anatomy. Changes in model rates due to the possible effects of dopamine loss listed above are compared with experiment. Our results suggest that a stronger indirect pathway, possibly combined with a weakened direct pathway, is compatible with empirical evidence. However, altered corticostriatal connection strengths are probably not solely responsible for substantially increased STN activity often found. A lower STN firing threshold, weaker intracortical inhibition, and stronger striato-GPe inhibition help explain the relatively large increase in STN rate. Reduced GPe-GPe inhibition and a lower GPe firing threshold can account for the comparatively small decrease in GPe rate frequently observed. Changes in cortex, GPe, and STN help normalize the cortical rate, also in accord with experiments. The model integrates the basal ganglia into a unified framework along with an existing thalamocortical model that already accounts for a wide range of electrophysiological phenomena. A companion paper discusses the dynamics and oscillations of this combined system.     

A model of the basal ganglia in voluntary movement and postural reactions

A basal ganglia central pattern generator (CPG) is developed and its role in voluntary movements on the ground and postural reactions on a disturbed platform are studied and analysed by simulation. Biped dynamics and platform kinematics are utilised. The effects of agonist–antagonist muscular co-activation and joint stiffness are formulated. The implementation of the necessary counter-manoeuvres for maintaining balance and postural stability is studied. A control strategy, applicable to large systems, is formulated. The biped manoeuvres and transitions terminate in pre-specified intervals of time. Gravity is included and compensated for. Certain voluntary and postural adjustment strategies are the same but are initiated differently. Further experimental/computational research may identify the central nervous system and sensory paths that lead to the CPG. All actuator forces linearly evolve in time from their original values to their terminal values. There are no central continuous feedback loops present. Monitoring and sensing, however, are ongoing. The counter-manoeuvres are based on learned human-like voluntary movements that are triggered by the disturbance. The required central inputs to the musculoskeletal system are designed in the CPG. A functional structure for the CPG is proposed. The effect of certain disorders and malfunctions of the CPG are studied by simulation.     

A population level computational model of the basal ganglia that generates parkinsonian local field potential activity

Recordings from the basal ganglia’s subthalamic nucleus are acquired via microelectrodes immediately prior to the application of Deep Brain Stimulation (DBS) treatment for Parkinson’s Disease (PD) to assist in the selection of the final point for the implantation of the DBS electrode. The acquired recordings reveal a persistent characteristic beta band peak in the power spectral density function of the Local Field Potential (LFP) signals. This peak is considered to lie at the core of the causality–effect relationships of the parkinsonian pathophysiology. Based on LFPs acquired from human subjects during DBS for PD, we constructed a computational model of the basal ganglia on the population level that generates LFPs to identify the critical pathophysiological alterations that lead to the expression of the beta band peak. To this end, we used experimental data reporting that the strengths of the synaptic connections are modified under dopamine depletion. The hypothesis that the altered dopaminergic modulation may affect both the amplitude and the time course of the postsynaptic potentials is validated by the model. The results suggest a pivotal role of both of these parameters to the pathophysiology of PD.     

A neural model for generating and learning a rapid movement sequence

 In this article, a neural model for generating and learning a rapid ballistic movement sequence in two-dimensional (2D) space is presented and evaluated in the light of some considerations about handwriting generation. The model is based on a central nucleus (called a planning space) consisting of a fully connected grid of leaky integrators simulating neurons, and reading an input vector Ξ (t) which represents the external movement of the end effector. The movement sequencing results in a succession of motor strokes whose instantiation is controlled by the global activation of the planning space as defined by a competitive interaction between the neurons of the grid. Constraints such as spatial accuracy and movement time are exploited for the correct synchronization of the impulse commands. These commands are then fed into a neuromuscular synergy whose output is governed by a delta lognormal equation. Each movement sequence is memorized originally as a symbolic engram representing the sequence of the principal reference points of the 2D movement. These points, called virtual targets, correspond to the targets of each single rapid motor stroke composing the movement sequence. The task during the learning phase is to detect the engram corresponding to a new observed movement; the process is controlled by the dynamics of the neural grid. Received: 16 March 1995/Accepted in revised form: 25 July 1995     

A neural network model of basal ganglia’s decision-making circuitry

The basal ganglia have been increasingly recognized as an important structure involved in decision making. Neurons in the basal ganglia were found to reflect the evidence accumulation process during decision making. However, it is not well understood how the direct and indirect pathways of the basal ganglia work together for decision making. Here, we create a recurrent neural network model that is composed of the direct and indirect pathways and test it with the classic random dot motion discrimination task. The direct pathway drives the outputs, which are modulated through a gating mechanism controlled by the indirect pathway. We train the network to learn the task and find that the network reproduces the accuracy and reaction time patterns of previous animal studies. Units in the model exhibit ramping activities that reflect evidence accumulation. Finally, we simulate manipulations of the direct and indirect pathways and find that the manipulations of the direct pathway mainly affect the choice while the manipulations of the indirect pathway affect the model’s reaction time. These results suggest a potential circuitry mechanism of the basal ganglia’s role in decision making with predictions that can be tested experimentally in the future.     

Simulander: A neural network model for the orientation movement of salamanders

Simulander is a feedforward neural network simulating the orientation movement of salamanders. The orientation movement is part of the prey capture behavior; it is performed with the head alone. Simulander is a network which consists of 300 neurons incorporating several cytoarchitectonic and electrophysiological features of the salamander brain. The network is trained by means of an evolution strategy. Although only 100 tectum neurons with fairly large receptive fields are used (coarse coding), Simulander is able to localize an irregularly moving prey precisely. It is demonstrated that large receptive field neurons are important for successful prey localization. The removal of a model tectum hemisphere leads to a network which accounts for investigations made in living monocular salamanders. The model also yields an understanding of electrical stimulation experiments in toads.     

A dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories

As a dynamical model for motor cortical activity during hand movement we consider an artificial neural network that consists of extensively interconnected neuron-like units and performs the neuronal population vector operations. Local geometrical parameters of a desired curve are introduced into the network as an external input. The output of the model is a time-dependent direction and length of the neuronal population vector which is calculated as a sum of the activity of directionally tuned neurons in the ensemble. The main feature of the model is that dynamical behavior of the neuronal population vector is the result of connections between directionally tuned neurons rather than being imposed externally. The dynamics is governed by a system of coupled nonlinear differential equations. Connections between neurons are assigned in the simplest and most common way so as to fulfill basic requirements stemming from experimental findings concerning the directional tuning of individual neurons and the stabilization of the neuronal population vector, as well as from previous theoretical studies. The dynamical behavior of the model reveals a close similarity with the experimentally observed dynamics of the neuronal population vector. Specifically, in the framework of the model it is possible to describe a geometrical curve in terms of the time series of the population vector. A correlation between the dynamical behavior of the direction and the length of the population vector entails a dependence of the neural velocity on the curvature of the tracing trajectory that corresponds well to the experimentally measured covariation between tangential velocity and curvature in drawing tasks.On leave of absencefrom the Institute of Molecular Genetics, Russian Academy of Sciences, Moscow, Russia.     

A hypothetical role of cortico-basal ganglia-thalamocortical loops in visual processing

The goal of the present work was to define the mechanisms underlying the contribution of sensory and limbic cortico-basal ganglia-thalamocortical loops to visual processing and its attentional modulation. We proposed that visual processing is promoted by dopamine-dependent long-term modifications of synaptic transmission in the basal ganglia that favour a selection of neocortical patterns representing a visual stimulus. This selection is the result of the opposite sign of modulation of strong and weak cortico-basal ganglia inputs and subsequent activity reorganization in each loop. Reorganization leads to disinhibition/inhibition of cortical neurons strongly/weakly excited by stimulus during dopamine release. Recruitment of the thalamo-basal ganglia-collicular pathway is proposed to be necessary for stimulus-evoked dopamine release that underlies bottom-up attentional effects. Visual excitation of the prefrontal cortex and hippocampus (via the thalamus), their cooperation in control of the basal ganglia and dopaminergic cell firing, and simultaneous modulation of activity in diverse cortico-basal ganglia-thalamocortical loops is proposed to underlie top-down attentional effects. It follows from our model that only those components of cortical responses can be modulated by attention, whose onset exceeds the latency of visual responses of dopaminergic cells (50-110 ms). This and other consequences of the model are in accordance with known experimental data.     

Presence of tetrahydroisoquinoline and 2-methyl-tetrahydroquinoline in parkinsonian and normal human brains

1,2,3,4-Tetrahydroisoquinoline (TIQ) and 2-methyl-1,2,3,4-tetrahydroquinoline (2-Me-TQ) were identified for the first time by gas chromatography-mass spectrometry in the parkinsonian and normal human brains. TIQ, an analogue of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), was markedly increased in the parkinsonian brain and could be an endogenous neurotoxin to induce Parkinson's disease.     

Circadian dysfunction in a rotenone-induced parkinsonian rodent model

Parkinson's disease (PD) is a neurodegenerative disorder that also involves circadian rhythm alterations. Modifications of circadian rhythm parameters have been shown to occur in both PD patients and toxin-induced PD animal models. In the latter case, rotenone, a potent inhibitor of mitochondrial complex I (nicotinamide adenine dinucleotide [NADH]-quinone reductase), has been used to elicit degeneration of dopaminergic neurons and development of parkinsonian syndrome. The present work addresses alterations induced by rotenone on both locomotor and body temperature circadian rhythms in rats. Rotenone-treated rats exhibited abnormalities in equilibrium, postural instability, and involuntary movements. Long-term subcutaneous administration of rotenone significantly reduced mean daily locomotor activity in most animals. During rotenone administration, mean body temperatures (BTs) and BT rhythm amplitudes were significantly lower than those observed in the control group. After long-term rotenone administration, the circadian rhythms of both locomotor activity (LA) and BT displayed decreased amplitudes, lower interdaily phase stability, and higher rhythm fragmentation, as compared to the control rats. The magnitude of the LA and BT circadian rhythm alterations induced by rotenone positively correlated with degree of motor impairment. These results indicate that rotenone induces circadian dysfunction in rats through some of the same mechanisms as those responsible for the development of motor disturbances.     

Regional distribution of vasoactive intestinal peptide in brains from normal and parkinsonian subjects

The distribution of vasoactive intestinal peptide (VIP) in the post-mortem human brain was determined by radioimmunoassay using a highly specific antiserum. The detection limit of the assay was 4 fmol/tube. The highest concentrations of VIP were found in the cerebral cortex, amygdala, hypothalamus and hippocampus. The lowest levels of peptide were detected in basal ganglia including caudate nucleus, external pallidum, putamen and substantia nigra. All dilution curves of acetic acid extracts from different brain areas were strictly parallel to the standard curve. Sephadex G-50 gel filtration of frontal cortex extract showed that VIP-like immunoreactivity (VIP-LI) eluted as a major peak comigrating with synthetic hVIP. Detailed mapping of VIP in the human cerebral cortex showed the existence of a rostro-caudal gradient of VIP-LI concentrations: the frontal cortex exhibited the highest VIP levels, the parietal and temporal cortex contained medium values and the occipital cortex contained the lowest VIP levels. The concentrations of VIP-LI were compared in various regions of the human brain from normal and parkinsonian subjects. No significant changes in VIP-LI levels occurred in the brains of patients dying with Parkinson's disease. No difference in VIP levels could be found either when the parkinsonian group was subdivided into nondemented and demented patients. These data indicate that VIP-containing neurons are not affected in parkinsonian patients. Our results also suggest that VIP neuronal systems are not involved in the course of dementing process in Parkinson's disease.     

The role of the basal ganglia in exploration in a neural model based on reinforcement learning

We present a computational model of basal ganglia as a key player in exploratory behavior. The model describes exploration of a virtual rat in a simulated water pool experiment. The virtual rat is trained using a reward-based or reinforcement learning paradigm which requires units with stochastic behavior for exploration of the system's state space. We model the Subthalamic Nucleus-Globus Pallidus externa (STN-GPe) segment of the basal ganglia as a pair of neuronal layers with oscillatory dynamics, exhibiting a variety of dynamic regimes such as chaos, traveling waves and clustering. Invoking the property of chaotic systems to explore state-space, we suggest that the complex exploratory dynamics of STN-GPe system in conjunction with dopamine-based reward signaling from the Substantia Nigra pars compacta (SNc) present the two key ingredients of a reinforcement learning system.     

A mechanobiological model of orthodontic tooth movement

Orthodontic tooth movement is achieved by the process of repeated alveolar bone resorption on the pressure side and new bone formation on the tension side. In order to optimize orthodontic treatment, it is important to identify and study the biological processes involved. This article presents a mechanobiological model using partial differential equations to describe cell densities, growth factor concentrations, and matrix densities occurring during orthodontic tooth movement. We hypothesize that such a model can predict tooth movement based on the mechanobiological activity of cells in the PDL. The developed model consists of nine coupled non-linear partial differential equations, and two distinct signaling pathways were modeled: the RANKL–RANK–OPG pathway regulating the communication between osteoblasts and osteoclasts and the TGF-β pathway mediating the differentiation of mesenchymal stem cells into osteoblasts. The predicted concentrations and densities were qualitatively validated by comparing the results to experiments reported in the literature. In the current form, the model supports our hypothesis, as it is capable of conceptually simulating important features of the biological interactions in the alveolar bone—PDL complex during orthodontic tooth movement.     

A dynamic model of motor basal ganglia functions

 Fast aiming movements were measured in a choice reaction paradigm in a healthy control group and in Parkinsonian patients. The patients were tested without (‘off ’) and with 3,4-dihydroxyphenylalanine (‘on’) (L-dopa) medication. The movement trajectories were used to estimate the parameters of a dynamic linear model. The model is based on the functional structure of the basal ganglia-thalamocortical circuit with direct and indirect pathways linking the putamen to the basal ganglia output nuclei (Albin et al. 1989). The output of the circuit is connected to a model for the motor neuron-musculo-skeletal system. The gain k _d for the direct pathway and the gain k _i for the indirect pathway were estimated. They were found to be significantly decreased for Parkinsonian patients in ‘off ’ compared with the control group. L-dopa therapy in Parkinsonian patients increased the gains of the direct and the indirect pathway almost to normal values which implies that the long-term dopamine level in the striatum was excitatory for the direct and for the indirect pathway. This result is restricted to movements of correct size. For movements of diminished size, which are typical for Parkinsonian patients, the model predicts that the dopamine level in the striatum is excitatory for the direct pathway but inhibitory for the indirect pathway. The simulated values for neuronal activities are in agreement with expected values according to the experimental data. The proposed model of the ‘motor’ basal ganglia thalamocortical circuit implies that information about biomechanical properties of the musculo-skeletal system is stored in the ‘motor’ basal ganglia-thalamocortical circuit, and that the basal ganglia are involved in computation of the desired movement amplitude. Received: 24 April 1996/Accepted in revised form: 25 February 1997     

A comparative study of a theoretical neural net model with MEG data from epileptic patients and normal individuals

Objective  

The aim of this study was to compare a theoretical neural net model with MEG data from epileptic patients and normal individuals.