Optimization of an anatomically and electrically detailed rodent subthalamic nucleus neuron model.

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an effective treatment for Parkinson's disease, but its mechanisms of action remain unclear. Detailed multicompartment computational models of STN neurons are often used to study how DBS electric fields modulate the neurons. However, currently available STN neuron models have some limitations in their biophysical realism. In turn, the goal of this study was to update a detailed rodent STN neuron model originally developed by Gillies and Willshaw in 2006. Our design requirements consisted of explicitly representing an axon connected to the neuron and updating the ion channel distributions based on the experimental literature to match established electrophysiological features of rodent STN neurons. We found that adding an axon to the STN neuron model substantially altered its firing characteristics. We then used a genetic algorithm to optimize biophysical parameters of the model. The updated model exhibited spontaneous firing, action potential shape, hyperpolarization response, and frequency-current curve that aligned well with experimental recordings from STN neurons. Subsequently, we evaluated the general compatibility of the updated biophysics by applying them to 26 different STN neuron morphologies derived from three-dimensional anatomical reconstructions. The different morphologies affected the firing behavior of the model, but the updated biophysics were robustly capable of maintaining the desired electrophysiological features. The new STN neuron model developed in this work offers a valuable tool for studying STN neuron firing properties and may find application in simulating STN local field potentials and analyzing the effects of STN DBS.NEW & NOTEWORTHY This study presents an anatomically and biophysically realistic rodent STN neuron model. The work showcases the use of a genetic algorithm to optimize the model parameters. We noted a substantial influence of the axon on the electrophysiological characteristics of STN neurons. The updated model offers a valuable tool to investigate the firing of STN neurons and their modulation by intrinsic and/or extrinsic factors.

Coupled Activation of the Hyperdirect and Cerebellothalamic Pathways with Zona Incerta Deep Brain Stimulation.

BACKGROUND: Deep brain stimulation (DBS) of the subthalamic nucleus (STN) or ventral intermediate nucleus (VIM) are established targets for the treatment of Parkinson's disease (PD) or essential tremor (ET), respectively. However, DBS of the zona incerta (ZI) can be effective for both disorders. VIM DBS is assumed to achieve its therapeutic effect via activation of the cerebellothalamic (CBT) pathway, whereas the activation of the hyperdirect (HD) pathway likely plays a role in the mechanisms of STN DBS. Interestingly, HD pathway axons also emit collaterals to the ZI and red nucleus (RN) and the CBT pathway courses nearby to the ZI. OBJECTIVE: The aim was to examine the ability of ZI DBS to mutually activate the HD and CBT pathways in a detailed computational model of human DBS. METHODS: We extended a previous model of the human HD pathway to incorporate axon collaterals to the ZI and RN. The anatomical framework of the model system also included representations of the CBT pathway and internal capsule (IC) fibers of passage. We then performed detailed biophysical simulations to quantify DBS activation of the HD, CBT, and IC pathways with electrodes located in either the STN or ZI. RESULTS: STN DBS and ZI DBS both robustly activated the HD pathway. However, STN DBS was limited by IC activation at higher stimulus amplitudes. Alternatively, ZI DBS avoided IC activation while simultaneously activating the HD and CBT pathways. CONCLUSIONS: From both neuroanatomical and biophysical perspectives, ZI DBS represents an advantageous target for coupled activation of the HD and CBT pathways. © 2024 International Parkinson and Movement Disorder Society.

Estimations of Charge Deposition Onto Convoluted Axon Surfaces Within Extracellular Electric Fields.

OBJECTIVE: Biophysical models of neural stimulation are a valuable approach to explaining the mechanisms of neuronal recruitment via applied extracellular electric fields. Typically, the applied electric field is estimated via a macroscopic finite element method solution and then applied to cable models as an extracellular voltage source. However, the field resolution is limited by the finite element size (typically 10's-100's of times greater than average neuronal cross-section). As a result, induced charges deposited onto anatomically realistic curved membrane interfaces are not taken into consideration. However, these details may alter estimates of the applied electric field and predictions of neural tissue activation. METHODS: To estimate microscopic variations of the electric field, data for intra-axonal space segmented from 3D scanning electron microscopy of the mouse brain genu of corpus callosum were used. The boundary element fast multipole method was applied to accurately compute the extracellular solution. Neuronal recruitment was then estimated via an activating function. RESULTS: Taking the physical structure of the arbor into account generally predicts higher values of the activating function. The relative integral 2-norm difference is 90% on average when the entire axonal arbor is present. A large fraction of this difference might be due to the axonal body itself. When an isolated physical axon is considered with all other axons removed, the relative integral 2-norm difference between the single-axon solution and the complete solution is 25% on average. CONCLUSION: Our result may provide an explanation as to why Deep Brain Stimulation experiments typically predict lower activation thresholds than commonly used FEM/Cable model approaches to predicting neuronal responses to extracellular electrical stimulation. SIGNIFICANCE: These results may change methods for bi-domain neural modeling and neural excitation.

Influence of charges deposited on membranes of human hyperdirect pathway axons on depolarization during subthalamic deep brain stimulation.

Objective.The motor hyperdirect pathway (HDP) is a key target in the treatment of Parkinson's disease with deep brain stimulation (DBS). Biophysical models of HDP DBS have been used to explore the mechanisms of stimulation. Built upon finite element method volume conductor solutions, such models are limited by a resolution mismatch, where the volume conductor is modeled at the macro scale, while the neural elements are at the micro scale. New techniques are needed to better integrate volume conductor models with neuron models.Approach.We simulated subthalamic DBS of the human HDP using finely meshed axon models to calculate surface charge deposition on insulting membranes of nonmyelinated axons. We converted the corresponding double layer extracellular problem to a single layer problem and applied the well-conditioned charge-based boundary element fast multipole method (BEM-FMM) with unconstrained numerical spatial resolution. Commonly used simplified estimations of membrane depolarization were compared with more realistic solutions.Main result.Neither centerline potential nor estimates of axon recruitment were impacted by the estimation method used except at axon bifurcations and hemispherical terminations. Local estimates of axon polarization were often much higher at bifurcations and terminations than at any other place along the axon and terminal arbor. Local average estimates of terminal electric field are higher by 10%-20%.Significance. Biophysical models of action potential initiation in the HDP suggest that axon terminations are often the lowest threshold elements for activation. The results of this study reinforce that hypothesis and suggest that this phenomenon is even more pronounced than previously realized.

Evolving characterization of the human hyperdirect pathway.

The hyperdirect pathway (HDP) represents the main glutamatergic input to the subthalamic nucleus (STN), through which the motor and prefrontal cerebral cortex can modulate basal ganglia activity. Further, direct activation of the motor HDP is thought to be an important component of therapeutic deep brain stimulation (DBS), mediating the disruption of pathological oscillations. Alternatively, unintended recruitment of the prefrontal HDP may partly explain some cognitive side effects of DBS therapy. Previous work describing the HDP has focused on non-human primate (NHP) histological pathway tracings, diffusion-weighted MRI analysis of human white matter, and electrophysiology studies involving paired cortical recordings with DBS. However, none of these approaches alone yields a complete understanding of the complexities of the HDP. As such, we propose that generative modeling methods hold promise to bridge anatomy and physiology results, from both NHPs and humans, into a more detailed representation of the human HDP. Nonetheless, numerous features of the HDP remain to be experimentally described before model-based methods can simulate corticosubthalamic activity with a high degree of scientific detail. Therefore, the goals of this review are to examine the experimental evidence for HDP projections from across the primate neocortex and discuss new data which are required to improve the utility of anatomical and biophysical models of the human corticosubthalamic system.

Subthalamic deep brain stimulation of an anatomically detailed model of the human hyperdirect pathway.

The motor hyperdirect pathway (HDP) is considered a key target in the treatment of Parkinson's disease with subthalamic deep brain stimulation (DBS). This hypothesis is partially derived from the association of HDP activation with evoked potentials (EPs) generated in the motor cortex and subthalamic nucleus (STN) after a DBS pulse. However, the biophysical details of how and when DBS-induced action potentials (APs) in HDP neurons reach their terminations in the cortex or STN remain unclear. Therefore, we used an anatomically detailed representation of the motor HDP, as well as the internal capsule (IC), in a model of human subthalamic DBS to explore AP activation and transmission in the HDP and IC. Our results show that small diameter HDP axons exhibited AP initiation in their subthalamic terminal arbor, which resulted in relatively long transmission latencies to cortex (∼3.5-8 ms). Alternatively, large diameter HDP axons were most likely to be directly activated in the capsular region, which resulted in short transmission times to the cortex (∼1-3 ms). However, those large diameter HDP antidromic APs would be indistinguishable from any other IC axons that were also activated by the stimulus. Conversely, DBS-induced APs in both small and large diameter HDP axons reached their synaptic boutons in the STN with similar timings, but both spanned a wide temporal range (∼0.5-5 ms). We also found that using anodic or bipolar stimulation helped to bias activation of the HDP over the IC. These computational results provide useful information for linking HDP activation with EP recordings in clinical experiments.NEW & NOTEWORTHY We used biophysical models to study pathway recruitment and conduction latencies of the hyperdirect pathway (HDP) in response to subthalamic deep brain stimulation (DBS). The model system allowed us to assess the influence of increased anatomical realism on pathway activity and the possibility of identifying HDP activity in evoked potentials (EPs) recorded in either the subthalamic nucleus (STN) or cortex. The model predicts that HDP activation is accentuated by complex axonal branching in the STN.

Histology-driven model of the macaque motor hyperdirect pathway.

Emerging appreciation for the hyperdirect pathway (HDP) as an important cortical glutamatergic input to the subthalamic nucleus (STN) has motivated a wide range of recent investigations on its role in motor control, as well as the mechanisms of subthalamic deep brain stimulation (DBS). However, the pathway anatomy and terminal arbor morphometry by which the HDP links cortical and subthalamic activity are incompletely understood. One critical hindrance to advancing understanding is the lack of anatomically detailed population models which can help explain how HDP pathway anatomy and neuronal biophysics give rise to spatiotemporal patterns of stimulus-response activity observed in vivo. Therefore, the goal of this study was to establish a population model of motor HDP axons through application of generative algorithms constrained by recent histology and imaging data. The products of this effort include a de novo macaque brain atlas, detailed statistical analysis of histological reconstructions of macaque motor HDP axons, and the generation of 10,000 morphometrically constrained synthetic motor HDP axons. The synthetic HDP axons exhibited a 3.8% mean error with respect to parametric distributions of the fiber target volume, total length, number of bifurcations, bifurcation angles, meander angles, and segment lengths measured in BDA-labeled HDP axon reconstructions. As such, this large population of synthetic motor HDP axons represents an anatomically based foundation for biophysical simulations that can be coupled to electrophysiological and/or behavioral measurements, with the goal of better understanding the role of the HDP in motor system activity.

Admittance Method for Estimating Local Field Potentials Generated in a Multi-Scale Neuron Model of the Hippocampus.

Significant progress has been made toward model-based prediction of neral tissue activation in response to extracellular electrical stimulation, but challenges remain in the accurate and efficient estimation of distributed local field potentials (LFP). Analytical methods of estimating electric fields are a first-order approximation that may be suitable for model validation, but they are computationally expensive and cannot accurately capture boundary conditions in heterogeneous tissue. While there are many appropriate numerical methods of solving electric fields in neural tissue models, there isn't an established standard for mesh geometry nor a well-known rule for handling any mismatch in spatial resolution. Moreover, the challenge of misalignment between current sources and mesh nodes in a finite-element or resistor-network method volume conduction model needs to be further investigated. Therefore, using a previously published and validated multi-scale model of the hippocampus, the authors have formulated an algorithm for LFP estimation, and by extension, bidirectional communication between discretized and numerically solved volume conduction models and biologically detailed neural circuit models constructed in NEURON. Development of this algorithm required that we assess meshes of (i) unstructured tetrahedral and grid-based hexahedral geometries as well as (ii) differing approaches for managing the spatial misalignment of current sources and mesh nodes. The resulting algorithm is validated through the comparison of Admittance Method predicted evoked potentials with analytically estimated LFPs. Establishing this method is a critical step toward closed-loop integration of volume conductor and NEURON models that could lead to substantial improvement of the predictive power of multi-scale stimulation models of cortical tissue. These models may be used to deepen our understanding of hippocampal pathologies and the identification of efficacious electroceutical treatments.

ROOTS: An Algorithm to Generate Biologically Realistic Cortical Axons and an Application to Electroceutical Modeling.

Advances in computation and neuronal modeling have enabled the study of entire neural tissue systems with an impressive degree of biological realism. These efforts have focused largely on modeling dendrites and somas while largely neglecting axons. The need for biologically realistic explicit axonal models is particularly clear for applications involving clinical and therapeutic electrical stimulation because axons are generally more excitable than other neuroanatomical subunits. While many modeling efforts can rely on existing repositories of reconstructed dendritic/somatic morphologies to study real cells or to estimate parameters for a generative model, such datasets for axons are scarce and incomplete. Those that do exist may still be insufficient to build accurate models because the increased geometric variability of axons demands a proportional increase in data. To address this need, a Ruled-Optimum Ordered Tree System (ROOTS) was developed that extends the capability of neuronal morphology generative methods to include highly branched cortical axon terminal arbors. Further, this study presents and explores a clear use-case for such models in the prediction of cortical tissue response to externally applied electric fields. The results presented herein comprise (i) a quantitative and qualitative analysis of the generative algorithm proposed, (ii) a comparison of generated fibers with those observed in histological studies, (iii) a study of the requisite spatial and morphological complexity of axonal arbors for accurate prediction of neuronal response to extracellular electrical stimulation, and (iv) an extracellular electrical stimulation strength-duration analysis to explore probable thresholds of excitation of the dentate perforant path under controlled conditions. ROOTS demonstrates a superior ability to capture biological realism in model fibers, allowing improved accuracy in predicting the impact that microscale structures and branching patterns have on spatiotemporal patterns of activity in the presence of extracellular electric fields.

Graph-Based Models of Cortical Axons for the Prediction of Neuronal Response to Extracellular Electrical Stimulation.

Over the past decade, many important insights to brain function have been obtained through clever application of detailed compartmental model neurons. New computing capabilities brought opportunities to study large networks of model neurons. Certain applications for these models, such as extracellular electrical stimulation, demand a very high degree of biological realism. While dendrites and somatic morphology may be obtained from explicit reconstructions, this approach is less useful for axonal structures, which are more difficult to characterize across a neuronal population. The purpose of this paper is to extend neuronal morphology generative models to highly branched axon terminal arbors as well as to present a clear use-case for such models in the study of cortical tissue response to externally applied electric fields. The results of this work are (i) presentation and quantitative/qualitative description of generated fibers and (ii) an extracellular electrical stimulation strength-duration study.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics.

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Model-Based Analysis of Electrode Placement and Pulse Amplitude for Hippocampal Stimulation.

OBJECTIVE: The ideal form of a neural-interfacing device is highly dependent upon the anatomy of the region with which it is meant to interface. Multiple-electrode arrays provide a system that can be adapted to various neural geometries. Computational models of stimulating systems have proven useful for evaluating electrode placement and stimulation protocols, but have yet to be adequately adapted to the unique features of the hippocampus. METHODS: As an approach to understanding potential memory restorative devices, an admittance method-NEURON model was constructed to predict the direct and synaptic response of a region of the rat dentate gyrus to electrical stimulation of the perforant path. RESULTS: A validation of estimated local field potentials against experimental recordings is performed and results of a bilinear electrode placement and stimulation amplitude parameter search are presented. CONCLUSION: The parametric analysis presented herein suggests that stimulating electrodes placed between the lateral and medial perforant path, near the crest of the dentate gyrus, yield a larger relative population response to given stimuli. SIGNIFICANCE: Beyond deepening understanding of the hippocampal tissue system, establishment of this model provides a method to evaluate candidate stimulating devices and protocols.

A large-scale detailed neuronal model of electrical stimulation of the dentate gyrus and perforant path as a platform for electrode design and optimization.

Owing to the dramatic rise in treatment of neurological disorders with electrical micro-stimulation it has become apparent that the major technological limitation in deploying effective devices lies in the process of designing efficient, safe, and outcome specific electrode arrays. The time-consuming and low-fidelity nature of gathering test data using experimental means and the immense control and flexibility of computational models, has prompted us and others to build models of electrical stimulation of neural networks that can be simulated in a computer. Because prior work has been focused on single cells, very small networks, or non-biological models of neural tissue, it was expedient that we take advantage of our, 4,040 processor, computing cluster to construct a large-scale 3-dimensional emulation of hippocampal tissue using detailed neuronal models with explicit and unique morphologies. This model, when paired with an equivalent circuit method of estimating voltage signal attenuation throughout anisotropic resistive tissue, can be used to predict tissue response to an exhaustive set of stimulation and tissue conditions: electrode geometry, array geometry, static dielectric properties of tissue, stimulation pulse features, etc. Preliminary experiments demonstrate that this system is capable of yielding neuronal responses with striking similarities to experimental results. This work provides an avenue to qualitative evaluation of electrode arrays, and more meaningful modeling of local field potentials in terms of their contributing sources and sinks.