Dynamics and Synchronization in Neuronal Models

La tesis está principalmente dedicada al modelado y simulación de sistemas neuronales. Entre otros aspectos se investiga el papel del ruido cuando actua sobre neuronas. El fenómeno de resonancia estocástica es caracterizado tanto a nivel teórico como reportado experimentalmente en un conjunto de neuronas del sistema motor. También se estudia el papel que juega la heterogeneidad en un conjunto de neuronas acopladas demostrando que la heterogeneidad en algunos parámetros de las neuronas puede mejorar la respuesta del sistema a una modulación periódica externa. También estudiamos del efecto de la topología y el retraso en las conexiones en una red neuronal. Se explora como las propiedades topológicas y los retrasos en la conducción de diferentes clases de redes afectan la capacidad de las neuronas para establecer una relación temporal bien definida mediante sus potenciales de acción. En particular, el concepto de consistencia se introduce y estudia en una red neuronal cuando plasticidad neuronal es tenida en cuenta entre las conexiones de la re

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential

Biological Pattern Generation: The Cellular and Computational Logic of Networks in Motion

In 1900, Ramón y Cajal advanced the neuron doctrine, defining the neuron as the fundamental signaling unit of the nervous system. Over a century later, neurobiologists address the circuit doctrine: the logic of the core units of neuronal circuitry that control animal behavior. These are circuits that can be called into action for perceptual, conceptual, and motor tasks, and we now need to understand whether there are coherent and overriding principles that govern the design and function of these modules. The discovery of central motor programs has provided crucial insight into the logic of one prototypic set of neural circuits: those that generate motor patterns. In this review, I discuss the mode of operation of these pattern generator networks and consider the neural mechanisms through which they are selected and activated. In addition, I will outline the utility of computational models in analysis of the dynamic actions of these motor networks

Computational Modeling of Spinal Cord Stimulation for Inspiratory Muscle Activation and Chronic Pain Management

Spinal cord stimulation (SCS) is a neuromodulation technique that applies electrical stimulation to the spinal cord to alter neural activity or processing. While SCS has historically been used as a last-resort therapy for chronic pain management, novel applications and technologies have recently been developed that either increase the efficacy of treatment for chronic pain or drive neural activity to produce muscular activity/movement following a paralyzing spinal cord injury (SCI). Despite these recent innovations, there remain fundamental questions concerning the neural recruitment underlying these efficacious results. This work evaluated the neural activity and mechanisms for three SCS applications: both conventional SCS and closed-loop SCS for pain management, as well as ventral, high frequency spinal cord stimulation (HF-SCS) for inspiratory muscle activation following a SCI. I developed computational models to both predict the neural response to SCS and explore factors influencing neural activation. Models consisted of three components: a finite element model (FEM) of the spinal cord to predict the potential fields generated by stimulation, biophysical neuron models, and algorithms to apply time-dependent extracellular potentials to the neuron models and simulate their response. While this cutting-edge modeling methodology could be used to predict neural activity following stimulation, it was unclear how anatomical and technical factors affected neural predictions. To evaluate these factors, I designed an FEM of a T9 thoracic spine with an implanted electrode array. Then, I sequentially removed details from the model and quantified the changes in neural predictions. I identified several factors with large (>30%) effects on neural thresholds, including overall electrode impedance (for voltage-controlled stimulation), the electrode position relative to the spine, and dura mater conductivity. This work will be invaluable for basic science and clinical applications of SCS. Next, I developed a canine model to evaluate T2 ventral HF-SCS for inspiratory muscle activation after an SCI. This model infrastructure included two neuron populations hypothesized to lead to inspiratory behavior: ventrolateral funiculus fibers (VLF) leading to diaphragm activation and inspiratory intercostal motoneurons. With this model, I predicted robust VLF and T2-T5 motoneuron recruitment within the experimental range of stimulation. I used this model framework to optimize several design parameters related to HF-SCS for inspiration. The optimal lead design parameters were evaluated via in vivo experiments, which found excellent agreement with model predictions. This work expands our mechanistic understanding of this novel therapy, improves its implementation, and aids in future translational efforts towards human subjects. Finally, I developed a computational model to evaluate closed-loop SCS for chronic pain management. This work characterized the neural origins of the evoked compound action potential (ECAP), the controlling biomarker of closed-loop stimulation. This modeling work showed that ECAP properties depend on activation of a narrow range of axon diameters and quantified how anatomical and stimulation factors (e.g., CSF thickness, stimulation configuration, lead position, pulse width) influence ECAP morphology, timing, and neural recruitment. These results improve our mechanistic understanding of closed-loop stimulation and neural recruitment during SCS. In summary, this dissertation work improves the methodology, validation, and applications of computational models of SCS. It also has direct applications to the clinical/pre-clinical implementation of SCS and may be invaluable for expanding the utility and efficacy of several treatments. The improved mechanistic understandings of neural activation described in this work may also aid in the future development of these therapies.PHDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169928/1/hzander_1.pd

The Mauthner Cell Half a Century Later: A Neurobiological Model for Decision-Making?

The Mauthner (M) cell is a critical element in a vital escape “reflex” triggered by abrupt or threatening events. Its properties at the molecular and synaptic levels, their various forms of plasticity, and the design of its networks, are all well adapted for this survival function. They guarantee that this behavior is appropriately unilateral, variable, and unpredictable. The M cell sets the behavioral threshold, and, acting in concert with other elements of the brainstem escape network, determines when, where, and how the escape is executed

Analysis of motoneuron responses to composite synaptic volleys (computer simulation study)

This paper deals with the analysis of changes in motoneuron (MN) firing evoked by repetitively applied stimuli aimed toward extracting information about the underlying synaptic volleys. Spike trains were obtained from computer simulations based on a threshold-crossing model of tonically firing MN, subjected to stimulation producing postsynaptic potentials (PSPs) of various parameters. These trains were analyzed as experimental results, using the output measures that were previously shown to be most effective for this purpose: peristimulus time histogram, raster plot and peristimulus time intervalgram. The analysis started from the effects of single excitatory and inhibitory PSPs (EPSPs and IPSPs). The conclusions drawn from this analysis allowed the explanation of the results of more complex synaptic volleys, i.e., combinations of EPSPs and IPSPs, and the formulation of directions for decoding the results of human neurophysiological experiments in which the responses of tonically firing MNs to nerve stimulation are analyzed

ALS-induced Excitability Changes in Individual Motorneurons and the Spinal Motorneuron Network in SOD1-G93A Mice at Symptom Onset

Amyotrophic lateral sclerosis (ALS) is the most common motorneuron (MN) disease in adulthood. ALS is hallmarked by the progressive loss of MNs in the brain, brainstem, and spinal cord. Many hypotheses to explain the pathogenesis of ALS have been explored, but the exact mechanisms underlying the development of this disease remain unknown. However, abnormalities in MN excitability and glutamate excitotoxicity are the most widely studied. For decades, researchers have examined MN excitability in ALS, but the current literature is inconsistent, showing evidence of hyperexcitability, hypoexcitability, or no change in excitability of MNs in ALS. Many of these studies also focus solely on the excitability of individual MNs, rather than the spinal MN network, whose output collectively drives muscle activity. Using electrophysiology intracellular and ventral root recordings in SOD1-G93AHigh-Copy (SOD) mice, the standard rodent model of ALS, at symptom onset, we demonstrate evidence of both hypo- and hyperexcitability in ALS, whereby disease mechanisms change MN excitability in one direction and compensatory mechanisms alter MN excitability in the opposite direction. Additionally, we show evidence of a novel mechanism contributing to the development of motor dysfunction in ALS at symptom onset, impaired sensorimotor integration. We also studied the effects of a novel treatment for ALS on MN excitability. In recent years, small-conductance calcium-activated potassium (SK) channels have been implicated in the pathogenesis of ALS. In MNs, these channels mediate the afterhyperpolarization (AHP) and synaptic transmission and plasticity and subsequently regulate MN excitability at the individual and network levels. In SOD mice, these channels are significantly reduced throughout disease progression and early treatment with an SK channel activator, CyPPA, restores these deficits. Early treatment with CyPPA also prolongs the survival and motor function of SOD mice. Our results demonstrate that the long-term therapeutic benefits of CyPPA in SOD mice are not due to alterations in MN excitability. SK channels are also implicated in neuroinflammation and microglia activation, mitochondrial dysfunction, and many other putative mechanisms related to ALS. Thus, deficits in one of these alternative molecular pathways is likely restored with early CyPPA treatment in SOD mice

Rhythmogenic and Premotor Functions of Dbx1 Interneurons in the Pre-Bötzinger Complex and Reticular Formation: Modeling and Simulation Studies

Breathing in mammals depends on rhythms that originate from the preBötzinger complex (preBötC) of the ventral medulla and a network of brainstem and spinal premotor neurons. The rhythm-generating core of the preBötC, as well as some premotor circuits, consists of interneurons derived from Dbx1-expressing precursors but the structure and function of these networks remain incompletely understood. We previously developed a cell-specific detection and laser ablation system to interrogate respiratory network structure and function in a slice model of breathing that retains the preBötC, premotor circuits, and the respiratory related hypoglossal (XII) motor nucleus such that in spontaneously rhythmic slices, cumulative ablation of Dbx1 preBötC neurons decreased XII motor output by half after only a few cell deletions, and then decelerated and terminated rhythmic function altogether as the tally increased. In contrast, cumulatively deleting Dbx1 premotor neurons decreased XII motor output monotonically, but did not affect frequency nor stop functionality regardless of the ablation tally. This dissertation presents several network modeling and cellular modeling studies that would further our understanding of how respiratory rhythm is generated and transmitted to the XII motor nucleus. First, we propose that cumulative deletions of Dbx1 preBötC neurons preclude rhythm by diminishing the amount of excitatory inward current or disturbing the process of recurrent excitation rather than structurally breaking down the topological network. Second, we establish a feasible configuration for neural circuits including an Erdős-Rényi preBötC network and a small-world reticular premotor network with interconnections following an anti-preferential attachment rule, which is the only configuration that produces consistent outcomes with previous experimental benchmarks. Furthermore, since the performance of neuronal network simulations is, to some extent, affected by the nature of the cellular model, we aim to develop a more realistic cellular model based on the one we adopted in previous network studies, which would account for some recent experimental findings on rhythmogenic preBötC neurons