Computational models advance deep brain stimulation for Parkinson's disease.

Deep brain stimulation(DBS) has become an effective intervention for advanced Parkinson's disease(PD), but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the basal ganglia (BG), the abnormal pathological changes of the BG in PD, and how computational models can help understand and advance DBS. We also describe two types of models: mathematical theoretical models and clinical predictive models. Mathematical theoretical models simulate neurons or neural networks of BG to shed light on the mechanistic principle underlying DBS, while clinical predictive models focus more on patients' outcomes, helping to adapt treatment plans for each patient and advance novel electrode designs. Finally, we provide insights and an outlook on future technologies.

Multi-timescale analysis of midbrain dopamine neuronal firing activities.

Midbrain dopamine (DA) neurons exhibit spiking and bursting patterns under physiological conditions. Based on the data on electrophysiological recordings, Yu et al. developed a 13-dimensional mathematical model to capture the detailed characteristics of the DA neuronal firing activities. We use the fitting method to simplify the original model into a 4-dimensional model. Then, the spiking-to-bursting transition is detected from a simple and robust mathematical condition. Physiologically, this condition is a balance of the restorative and the regenerative ion channels at resting potential. Geometrically, this condition imposes a transcritical bifurcation. Moreover, we combine singularity theory and singular perturbation methods to capture the geometry of three-timescale firing attractors in a universal unfolding of a cusp singularity. In particular, the planar description of the corresponding firing patterns can generate the corresponding firing attractors. This analysis provides a new idea for understanding the firing activities of the DA neuron and the specific mechanisms for the switching and dynamic regulation among different patterns.

Basal ganglia network dynamics and function: Role of direct, indirect and hyper-direct pathways in action selection.

Basal ganglia (BG) are a widely recognized neural basis for action selection, but its decision-making mechanism is still a difficult problem for researchers. Therefore, we constructed a spiking neural network inspired by the BG anatomical data. Simulation experiments were based on the principle of dis-inhibition and our functional hypothesis within the BG: the direct pathway, the indirect pathway, and the hyper-direct pathway of the BG jointly implement the initiation execution and termination of motor programs. Firstly, we studied the dynamic process of action selection with the network, which contained intra-group competition and inter-group competition. Secondly, we focused on the effects of the stimulus intensity and the proportion of excitation and inhibition on the GPi/SNr. The results suggested that inhibition and excitation shape action selection. They also explained why the firing rate of GPi/SNr did not continue to increase in the action-selection experiment. Finally, we discussed the experimental results with the functional hypothesis. Uniquely, this paper summarized the decision-making neural mechanism of action selection based on the direct pathway, the indirect pathway, and the hyper-direct pathway within BG.

Individual identification for different age groups using functional connectivity strength.

BACKGROUND AND PURPOSE: Many studies demonstrate individual differences in functional network, especially those with age. Meanwhile, aging is one of the potential risk factors for Alzheimer's disease. Therefore, it is important to explore the discrepant pattern in aging population. METHODS: Most existing methods mostly target ancient atlas for the extraction of the classification features and not consider the effect of global signal. We use two novel atlases for the extraction of classification features and then use the whole and intra-hemispheric functional connectivity strength (FCS) as classification parameters to classify different age groups, respectively. Meanwhile, the regression of global signal or not during the preprocessing has been considered. Next, the support vector machine-recursive feature elimination (SVM-RFE) method is applied for feature selection and the SVM method is applied for classification. In addition, the receiver operating characteristic curve and area under the curve are drawn to evaluate the robustness of classifier. Finally, the discriminative features are related to the physiological mechanism of aging. RESULTS: The promising classification performance exhibits that the FCS can effectively distinguish different age groups. Moreover, the SVM-RFE method can increase the accuracy and extract the discriminative features. The classifiers constructed by the features derived from different atlas receive similar classification performance. CONCLUSION: This study successfully distinguishes the young group, middle-aged group, and elderly group through FCS parameter, indicating the functional pattern of the network exists difference between three groups. Moreover, the results received by the SVM-RFE method and SVM classifier have the very good robustness and not specific to particular atlas and not affected by global signal and appropriate for the FCS of the whole brain or intra-hemisphere, which suggests that we can apply them to disease diagnosis in the future.

The Adjustment of Anterior Forebrain Pathway (AFP) to Birdsong Is Phased during Song Learning and Maintenance.

Anterior forebrain pathway (AFP), a basal ganglia-dorsal forebrain circuit, significantly impacts birdsong, specifically in juvenile or deaf birds. Despite many physiological experiments supporting AFP's role in song production, the mechanism underlying it remains poorly understood. Using a computational model of the anterior forebrain pathway and song premotor pathway, we examined the dynamic process and exact role of AFP during song learning and distorted auditory feedback (DAF). Our simulation suggests that AFP can adjust the premotor pathway structure and syllables based on its delayed input to the robust nucleus of the archistriatum (RA). It is also indicated that the adjustment to the synaptic conductance in the song premotor pathway has two phases: normal phases where the adjustment decreases with an increasing number of trials and abnormal phases where the adjustment remains stable or even increases. These two phases alternate and impel a specific effect on birdsong based on AFP's specific structures, which may be associated with auditory feedback. Furthermore, our model captured some characteristics shown in birdsong experiments, such as similarities in pitch, intensity, and duration to real birds and the highly abnormal features of syllables during DAF.

Bifurcation analysis of a Morris-Lecar neuron model.

In this paper, we investigate the dynamical behaviors of a Morris-Lecar neuron model. By using bifurcation methods and numerical simulations, we examine the global structure of bifurcations of the model. Results are summarized in various two-parameter bifurcation diagrams with the stimulating current as the abscissa and the other parameter as the ordinate. We also give the one-parameter bifurcation diagrams and pay much attention to the emergence of periodic solutions and bistability. Different membrane excitability is obtained by bifurcation analysis and frequency-current curves. The alteration of the membrane properties of the Morris-Lecar neurons is discussed.

Structural constraints on the emergence of oscillations in multi-population neural networks.

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

Dynamical properties of firing patterns in ELL pyramidal neuron under external electric field stimulus.

Pyramidal neurons in the electrosensory lateral line lobe (ELL) of weakly electric fish activate in an environment of time-varying electric fields, which are generated by the fish itself, while how these pyramidal neurons would behave or what kinds of firing patterns these neurons would produce under different electric fields is still unclear. In this research, the firing behaviors of ELL pyramidal neuron under DC and AC electric field stimulus are investigated in a two-compartment neuron model. By means of numerical simulations we show that firing patterns of the model ELL pyramidal neuron are much diverse under different values of DC electric field, and neuronal spike frequency exhibits a monotone decreasing trend with the linearly increased DC fields, moreover, the transition mode between these firing patterns with the variation of DC electric fields demonstrates an explicit periodic route. While for AC electric fields, neuronal firing frequency periodically transforms with the increase of AC frequency, particularly, a special transition pattern (from multi-period bursting to spiking) repeatedly appears with the change of AC frequency. Our simulation results indicate that ELL pyramidal neurons fire dynamically under the time-varying electric fields, the diversity of firing patterns and their periodic transition modes may imply the potential roles of these dynamical firings in the coding strategy of sensory information processing.

Elevated prelimbic cortex-to-basolateral amygdala circuit activity mediates comorbid anxiety-like behaviors associated with chronic pain.

Chronic pain can cause both hyperalgesia and anxiety symptoms. However, how the two components are encoded in the brain remains unclear. The prelimbic cortex (PrL), a critical brain region for both nociceptive and emotional modulations, serves as an ideal medium for comparing how the two components are encoded. We report that PrL neurons projecting to the basolateral amygdala (PrLBLA) and those projecting to the ventrolateral periaqueductal gray (PrLl/vlPAG) were segregated and displayed elevated and reduced neuronal activity, respectively, during pain chronicity. Consistently, optogenetic suppression of the PrL-BLA circuit reversed anxiety-like behaviors, whereas activation of the PrL-l/vlPAG circuit attenuated hyperalgesia in mice with chronic pain. Moreover, mechanistic studies indicated that elevated TNF-α/TNFR1 signaling in the PrL caused increased insertion of GluA1 receptors into PrLBLA neurons and contributed to anxiety-like behaviors in mice with chronic pain. Together, these results provide insights into the circuit and molecular mechanisms in the PrL for controlling pain-related hyperalgesia and anxiety-like behaviors.

Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance.

Neuronal membrane capacitance C (m) is one of the prominent factors in action potential initiation and propagation and then influences the firing patterns of neurons. Exploring the roles that C (m) plays in different firing patterns can facilitate the understanding of how different factors might influence neuronal firing behaviors. However, the impacts of variations in C (m) on neuronal firing patterns have been only partly explored until now. In this study, the influence of C (m) on burst firing behaviors of a two-compartment pyramidal neuron (including somatic compartment and dendritic compartment) was investigated by means of computer simulation, the value of C (m) in each compartment was denoted as C (m,s) and C (m,d), respectively. Two cases were considered, in the first case, we let C (m,s) =C (m,d), and then changed them simultaneously. While in the second case, we assumed C (m,s) ≠C (m,d), and then changed them, respectively. From the simulation results obtained from these two cases, it was found that the variation of C (m) in the somatic compartment and the dendritic compartment show much difference, simulated results obtained from the variation of C (m,d) have much more similarities than that of C (m,s) when comparing with the results obtained in the first case under which C (m,s) =C (m,d). These different effects of C (m,s) and C (m,d) on neuronal firing behaviors may result from the different topology and functional roles of soma and dendrites. Numerical results demonstrated in this paper may give us some inspiration in understanding the possible roles of C (m) in burst firing patterns, especially their transitions in compartmental neurons.

Model-based Quantitative optimization of deep brain stimulation and prediction of Parkinson's states.

Although the exact etiology of Parkinson's disease (PD) is still unknown, there are a variety of treatments available to alleviate its symptoms according to the development stage of PD. Deep brain stimulation (DBS), the most common surgical treatment for advanced PD, accurately locates and implants stimulating electrodes at specific targets in the brain to deliver high-frequency electrical stimulation that alters the excitability of the corresponding nuclei. However, for different patients and stages of PD development, there exists a choice of the optimal DBS protocol. In this paper, we propose a quantitative method (multi-dimensional feature indexes) to determine the stimulation pattern, stimulation parameters, and target of DBS from the perspective of the network model. On the other hand, based on this method, the development of PD can be predicted so that timely treatment can be given to patients. Simulation results show that, first, different network states can be distinguished by extracting features of the firing activity of neuronal populations within the basal ganglia network system. Secondly, the optimal DBS treatment can be selected by comparing the feature indexes vectors of the pre- and post-state of the network after the action of different modes of DBS. Lastly, the evolution of the network state from normal to pathological is simulated. The critical point of network state transitions is determined. These results provide a quantitative and qualitative method for determining the optimal regimen for DBS for PD, which is helpful for clinical practice.

Analysis of Hemichannels and Gap Junctions: Application and Extension of the Passive Transmembrane Ion Transport Model.

Electrical synaptic transmission is an essential form of interneuronal communication which is mediated by gap junctions that permit ion flow. Three gene families (connexins, innexins, and pannexins) have evolved to form gap junctional channels. Each gap junctional channel is formed by the docking of the hemichannel of one cell with the corresponding hemichannel of an adjacent cell. To date, there has been a lack of study models to describe this structure in detail. In this study, we demonstrate that numerical simulations suggest that the passive transmembrane ion transport model, based on the generality of ion channels, also applies to hemichannels in non-junctional plasma membranes. On this basis, we established a gap junctional channel model, which describes hemichannels' docking. We simulated homotypic and heterotypic gap junctions formed by connexins, innexins, and pannexins. Based on the numerical results and our theoretical model, we discussed the physiology of hemichannels and gap junctions, including ion blockage of hemichannels, voltage gating of gap junctions, and asymmetry and delay of electrical synaptic transmission, for which the numerical simulations are first comprehensively realized.

A geometric framework for understanding dynamic information integration in context-dependent computation.

The prefrontal cortex (PFC) plays a prominent role in performing flexible cognitive functions and working memory, yet the underlying computational principle remains poorly understood. Here, we trained a rate-based recurrent neural network (RNN) to explore how the context rules are encoded, maintained across seconds-long mnemonic delay, and subsequently used in a context-dependent decision-making task. The trained networks replicated key experimentally observed features in the PFC of rodent and monkey experiments, such as mixed selectivity, neuronal sequential activity, and rotation dynamics. To uncover the high-dimensional neural dynamical system, we further proposed a geometric framework to quantify and visualize population coding and sensory integration in a temporally defined manner. We employed dynamic epoch-wise principal component analysis (PCA) to define multiple task-specific subspaces and task-related axes, and computed the angles between task-related axes and these subspaces. In low-dimensional neural representations, the trained RNN first encoded the context cues in a cue-specific subspace, and then maintained the cue information with a stable low-activity state persisting during the delay epoch, and further formed line attractors for sensor integration through low-dimensional neural trajectories to guide decision-making. We demonstrated via intensive computer simulations that the geometric manifolds encoding the context information were robust to varying degrees of weight perturbation in both space and time. Overall, our analysis framework provides clear geometric interpretations and quantification of information coding, maintenance, and integration, yielding new insight into the computational mechanisms of context-dependent computation.

Episodic memory governs choices: An RNN-based reinforcement learning model for decision-making task.

Typical methods to study cognitive function are to record the electrical activities of animal neurons during the training of animals performing behavioral tasks. A key problem is that they fail to record all the relevant neurons in the animal brain. To alleviate this problem, we develop an RNN-based Actor-Critic framework, which is trained through reinforcement learning (RL) to solve two tasks analogous to the monkeys' decision-making tasks. The trained model is capable of reproducing some features of neural activities recorded from animal brain, or some behavior properties exhibited in animal experiments, suggesting that it can serve as a computational platform to explore other cognitive functions. Furthermore, we conduct behavioral experiments on our framework, trying to explore an open question in neuroscience: which episodic memory in the hippocampus should be selected to ultimately govern future decisions. We find that the retrieval of salient events sampled from episodic memories can effectively shorten deliberation time than common events in the decision-making process. The results indicate that salient events stored in the hippocampus could be prioritized to propagate reward information, and thus allow decision-makers to learn a strategy faster.

Corrigendum: A General Model of Ion Passive Transmembrane Transport Based on Ionic Concentration.

[This corrects the article DOI: 10.3389/fncom.2018.00110.].

Analysis of structural brain MRI and multi-parameter classification for Alzheimer's disease.

Incorporating with machine learning technology, neuroimaging markers which extracted from structural Magnetic Resonance Images (sMRI), can help distinguish Alzheimer's Disease (AD) patients from Healthy Controls (HC). In the present study, we aim to investigate differences in atrophic regions between HC and AD and apply machine learning methods to classify these two groups. T1-weighted sMRI scans of 158 patients with AD and 145 age-matched HC were acquired from the ADNI database. Five kinds of parameters (i.e. cortical thickness, surface area, gray matter volume, curvature and sulcal depth) were obtained through the preprocessing steps. The recursive feature elimination (RFE) method for support vector machine (SVM) and leave-one-out cross validation (LOOCV) were applied to determine the optimal feature dimensions. Each kind of parameter was trained by SVM algorithm to acquire a classifier, which was used to classify HC and AD ultimately. Moreover, the ROC curves were depicted for testing the classifiers' performance and the SVM classifiers of two-dimensional spaces took the top two important features as classification features for separating HC and AD to the maximum extent. The results showed that the decreased cortical thickness and gray matter volume dramatically exhibited the trend of atrophy. The key differences between AD and HC existed in the cortical thickness and gray matter volume of the entorhinal cortex and medial orbitofrontal cortex. In terms of classification results, an optimal accuracy of 90.76% was obtained via multi-parameter combination (i.e. cortical thickness, gray matter volume and surface area). Meanwhile, the receiver operating characteristic (ROC) curves and area under the curve (AUC) were also verified multi-parameter combination could reach a better classification performance (AUC=0.94) after the SVM-RFE method. The results could be well prove that multi-parameter combination could provide more useful classified features from multivariate anatomical structure than single parameter. In addition, as cortical thickness and multi-parameter combination contained more important classified information with fewer feature dimensions after feature selection, it could be optimum to separate HC from AD to take the top two important features of them to construct SVM classifiers in two-dimensional space. The proposed work is a promising approach suggesting an important role for machine-learning based diagnostic image analysis for clinical practice.

A General Model of Ion Passive Transmembrane Transport Based on Ionic Concentration.

Current mainstream neural computing is based on the electricity model proposed by Hodgkin and Huxley in 1952, the core of which is ion passive transmembrane transport controlled by ion channels. However, studies on the evolutionary history of ion channels have shown that some neuronal ion channels predate the neurons. Thus, to deepen our understanding of neuronal activities, ion channel models should be applied to other cells. Expanding the scope of electrophysiological experiments from nerve to muscle, animal to plant, and metazoa to protozoa, has lead the discovery of a number of ion channels. Moreover, the properties of these newly discovered ion channels are too complex to be described by current common models. Hence this paper has presented a convenient method for estimating the distribution of ions under an electric field and established a general ionic concentration-based model of ion passive transmembrane transport that is simple but capable of explaining and simulating the complex phenomena of patch clamp experiments, is applicable to different ion channels in different cells of different species, and conforms to the current general understanding of ion channels. Finally, we designed a series of mathematical experiments, which we have compared with the results of typical electrophysiological experiments conducted on plant cells, oocytes, myocytes, cardiomyocytes, and neurocytes, to verify the model.

Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise.

Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electrical activities of the Morris-Lecar (M-L) model with electromagnetic radiation or Gaussian white noise, which can restore the authenticity of neurons in realistic neural network. First, we explore dynamical response of the whole system with electromagnetic induction (EMI) and Gaussian white noise. We find that there are slight differences in the discharge behaviors via comparing the response of original system with that of improved system, and electromagnetic induction can transform bursting or spiking state to quiescent state and vice versa. Furthermore, we research bursting transition mode and the corresponding periodic solution mechanism for the isolated neuron model with electromagnetic induction by using one-parameter and bi-parameters bifurcation analysis. Finally, we analyze the effects of Gaussian white noise on the original system and coupled system, which is conducive to understand the actual discharge properties of realistic neurons.

The role of relative membrane capacitance and time delay in cerebellar Purkinje cells.

The membrane capacitance of a neuron can influence the synaptic efficacy and the speed of electrical signal propagation. Exploring the role of membrane capacitance will help facilitate a deeper understanding of the electrical properties of neurons. Thus, in this paper, we investigated the neuronal firing behaviors of a two-compartment model in Purkinje cells. We evaluated the influence of membrane capacitance under two different circumstances: in the absence of time delay and in the presence of time delay. Firstly, we separately studied the influence of somatic membrane capacitance Cs and dendritic membrane capacitance Cd on neuronal firing patterns. Through numerical simulation, we observed that they had two different types of period-adding scenarios, i.e. with and without chaotic bursting. Secondly, our results indicated that when the time delay was included in the model, periodic motions were more inclined to be destroyed, while at the same time, corresponding new chaotic motions were induced. These findings suggested that membrane capacitance and time delay play a pivotal functional role in modulating dynamical firing properties of neurons, especially aspects which lead to behaviors which result in changes to bursting patterns.

The Effects of Medium Spiny Neuron Morphologcial Changes on Basal Ganglia Network under External Electric Field: A Computational Modeling Study.

The damage of dopaminergic neurons that innervate the striatum has been considered to be the proximate cause of Parkinson's disease (PD). In the dopamine-denervated state, the loss of dendritic spines and the decrease of dendritic length may prevent medium spiny neuron (MSN) from receiving too much excitatory stimuli from the cortex, thereby reducing the symptom of Parkinson's disease. However, the reduction in dendritic spine density obtained by different experiments is significantly different. We developed a biological-based network computational model to quantify the effect of dendritic spine loss and dendrites tree degeneration on basal ganglia (BG) signal regulation. Through the introduction of error index (EI), which was used to measure the attenuation of the signal, we explored the amount of dendritic spine loss and dendritic trees degradation required to restore the normal regulatory function of the network, and found that there were two ranges of dendritic spine loss that could reduce EI to normal levels in the case of dopamine at a certain level, this was also true for dendritic trees. However, although these effects were the same, the mechanisms of these two cases were significant difference. Using the method of phase diagram analysis, we gained insight into the mechanism of signal degradation. Furthermore, we explored the role of cortex in MSN morphology changes dopamine depletion-induced and found that proper adjustments to cortical activity do stop the loss in dendritic spines induced by dopamine depleted. These results suggested that modifying cortical drive onto MSN might provide a new idea on clinical therapeutic strategies for Parkinson's disease.