A population model of deep brain stimulation in movement disorders from circuits to cells

Copyright © 2020 Yousif, Bain, Nandi and Borisyuk.For more than 30 years, deep brain stimulation (DBS) has been used to target the symptoms of a number of neurological disorders and in particular movement disorders such as Parkinson's disease (PD) and essential tremor (ET). It is known that the loss of dopaminergic neurons in the substantia nigra leads to PD, while the exact impact of this on the brain dynamics is not fully understood, the presence of beta-band oscillatory activity is thought to be pathological. The cause of ET, however, remains uncertain, however pathological oscillations in the thalamocortical-cerebellar network have been linked to tremor. Both of these movement disorders are treated with DBS, which entails the surgical implantation of electrodes into a patient's brain. While DBS leads to an improvement in symptoms for many patients, the mechanisms underlying this improvement is not clearly understood, and computational modeling has been used extensively to improve this. Many of the models used to study DBS and its effect on the human brain have mainly utilized single neuron and single axon biophysical models. We have previously shown in separate models however, that the use of population models can shed much light on the mechanisms of the underlying pathological neural activity in PD and ET in turn, and on the mechanisms underlying DBS. Together, this work suggested that the dynamics of the cerebellar-basal ganglia thalamocortical network support oscillations at frequency range relevant to movement disorders. Here, we propose a new combined model of this network and present new results that demonstrate that both Parkinsonian oscillations in the beta band and oscillations in the tremor frequency range arise from the dynamics of such a network. We find regions in the parameter space demonstrating the different dynamics and go on to examine the transition from one oscillatory regime to another as well as the impact of DBS on these different types of pathological activity. This work will allow us to better understand the changes in brain activity induced by DBS, and allow us to optimize this clinical therapy, particularly in terms of target selection and parameter setting.Peer reviewe

Mechanisms underlying the recruitment of inhibitory interneurons in fictive swimming in developing Xenopus laevis tadpoles

Funding: Authors thank BBSRC for funding this research (BB/L000814/1 to R.B.; BB/T003146 to W.L.).Developing spinal circuits generate patterned motor outputs while many neurons with high membrane resistances are still maturing. In the spinal cord of hatchling frog tadpoles of unknown sex, we found that the firing reliability in swimming of inhibitory interneurons with commissural and ipsilateral ascending axons was negatively correlated with their cellular membrane resistance. Further analyses showed that neurons with higher resistances had outward rectifying properties, low firing thresholds and little delay in firing evoked by current injections. Input synaptic currents these neurons received during swimming, either compoundˎ unitary current amplitudes or unitary synaptic current numbers, were scaled with their membrane resistances, but their own synaptic outputs were correlated with membrane resistances of their postsynaptic partners. Analyses of neuronal dendritic and axonal lengths and their activities in swimming and cellular input resistances did not reveal a clear correlation pattern. Incorporating these electrical and synaptic properties in a computer swimming model produced robust swimming rhythms whereas randomising input synaptic strengths led to the breakdown of swimming rhythms, coupled with less synchronised spiking in the inhibitory interneurons. We conclude that the recruitment of these developing interneurons in swimming can be predicted by cellular input resistances, but the order is opposite to the motor-strength based recruitment scheme depicted by Henneman’s size principle. This form of recruitment/integration order in development before the emergence of refined motor control is progressive potentially with neuronal acquisition of mature electrical and synaptic properties, among which the scaling of input synaptic strengths with cellular input resistance plays a critical role.PostprintPeer reviewe

Axon and dendrite geography predict the specificity of synaptic connections in a functioning spinal cord network

<p>Abstract</p> <p>Background</p> <p>How specific are the synaptic connections formed as neuronal networks develop and can simple rules account for the formation of functioning circuits? These questions are assessed in the spinal circuits controlling swimming in hatchling frog tadpoles. This is possible because detailed information is now available on the identity and synaptic connections of the main types of neuron.</p> <p>Results</p> <p>The probabilities of synapses between 7 types of identified spinal neuron were measured directly by making electrical recordings from 500 pairs of neurons. For the same neuron types, the dorso-ventral distributions of axons and dendrites were measured and then used to calculate the probabilities that axons would encounter particular dendrites and so potentially form synaptic connections. Surprisingly, synapses were found between all types of neuron but contact probabilities could be predicted simply by the anatomical overlap of their axons and dendrites. These results suggested that synapse formation may not require axons to recognise specific, correct dendrites. To test the plausibility of simpler hypotheses, we first made computational models that were able to generate longitudinal axon growth paths and reproduce the axon distribution patterns and synaptic contact probabilities found in the spinal cord. To test if probabilistic rules could produce functioning spinal networks, we then made realistic computational models of spinal cord neurons, giving them established cell-specific properties and connecting them into networks using the contact probabilities we had determined. A majority of these networks produced robust swimming activity.</p> <p>Conclusion</p> <p>Simple factors such as morphogen gradients controlling dorso-ventral soma, dendrite and axon positions may sufficiently constrain the synaptic connections made between different types of neuron as the spinal cord first develops and allow functional networks to form. Our analysis implies that detailed cellular recognition between spinal neuron types may not be necessary for the reliable formation of functional networks to generate early behaviour like swimming.</p

To swim or not to swim: A population-level model of Xenopus tadpole decision making and locomotor behaviour

We present a detailed computational model of interacting neuronal populations that mimic the hatchling Xenopus tadpole nervous system. The model includes four sensory pathways, integrators of sensory information, and a central pattern generator (CPG) network. Sensory pathways of different modalities receive inputs from an "environment"; these inputs are then processed and integrated to select the most appropriate locomotor action. The CPG populations execute the selected action, generating output in motor neuron populations. Thus, the model describes a detailed and biologically plausible chain of information processing from external signals to sensors, sensory pathways, integration and decision-making, action selection and execution and finally, generation of appropriate motor activity and behaviour. We show how the model produces appropriate behaviours in response to a selected scenario, which consists of a sequence of "environmental" signals. These behaviours might be relatively complex due to noisy sensory pathways and the possibility of spontaneous actions

The decision to move : response times, neuronal circuits and sensory memory in a simple vertebrate

All animals use sensory systems to monitor external events and have to decide whether to move. Response times are long and variable compared to reflexes, and fast escape movements. The complexity of adult vertebrate brains makes it difficult to trace the neuronal circuits underlying basic decisions to move. To simplify the problem, we investigate the nervous system and responses of hatchling frog tadpoles which swim when their skin is stimulated. Studying the neuron-by-neuron pathway from sensory to hindbrain neurons, where the decision to swim is made, has revealed two simple pathways generating excitation which sums to threshold in these neurons to initiate swimming. The direct pathway leads to short, and reliable delays like an escape response. The other includes a population of sensory processing neurons which extend firing to introduce noise and delay into responses. These neurons provide a brief, sensory memory of the stimulus, that allows tadpoles to integrate stimuli occurring within a second or so of each other. We relate these findings to other studies and conclude that sensory memory makes a fundamental contribution to simple decisions and is present in the brainstem of a basic vertebrate at a surprisingly early stage in development.PostprintPeer reviewe

A developmental approach to predicting neuronal connectivity from small biological datasets: a gradient-based neuron growth model.

PMCID: PMC3931784 Open Access article: BB/G006652/1 and BB/G006369/1.Relating structure and function of neuronal circuits is a challenging problem. It requires demonstrating how dynamical patterns of spiking activity lead to functions like cognitive behaviour and identifying the neurons and connections that lead to appropriate activity of a circuit. We apply a "developmental approach" to define the connectome of a simple nervous system, where connections between neurons are not prescribed but appear as a result of neuron growth. A gradient based mathematical model of two-dimensional axon growth from rows of undifferentiated neurons is derived for the different types of neurons in the brainstem and spinal cord of young tadpoles of the frog Xenopus. Model parameters define a two-dimensional CNS growth environment with three gradient cues and the specific responsiveness of the axons of each neuron type to these cues. The model is described by a nonlinear system of three difference equations; it includes a random variable, and takes specific neuron characteristics into account. Anatomical measurements are first used to position cell bodies in rows and define axon origins. Then a generalization procedure allows information on the axons of individual neurons from small anatomical datasets to be used to generate larger artificial datasets. To specify parameters in the axon growth model we use a stochastic optimization procedure, derive a cost function and find the optimal parameters for each type of neuron. Our biologically realistic model of axon growth starts from axon outgrowth from the cell body and generates multiple axons for each different neuron type with statistical properties matching those of real axons. We illustrate how the axon growth model works for neurons with axons which grow to the same and the opposite side of the CNS. We then show how, by adding a simple specification for dendrite morphology, our model "developmental approach" allows us to generate biologically-realistic connectomes

A simple decision to move in response to touch reveals basic sensory memory and mechanisms for variable response times

Many motor responses to sensory input, like locomotion or eye movements, are much slower than reflexes. Can simpler animals provide fundamental answers about the cellular mechanisms for motor decisions? Can we observe the ‘accumulation’ of excitation to threshold proposed to underlie decision making elsewhere? We explore how somatosensory touch stimulation leads to the decision to swim in hatchling Xenopus tadpoles. Delays measured to swimming in behaving and immobilized tadpoles are long and variable. Activity in their extensively studied sensory and sensory pathway neurons is too short-lived to explain these response delays. Instead, whole-cell recordings from the hindbrain reticulospinal neurons that drive swimming show these receive prolonged, variable synaptic excitation lasting for nearly a second following a brief stimulus. They fire and initiate swimming when this excitation reaches threshold. Analysis of the summation of excitation requires us to propose extended firing in currently undefined presynaptic hindbrain neurons. Simple models show that a small excitatory recurrent-network inserted in the sensory pathway can mimic this process. We suggest that such a network may generate slow, variable summation of excitation to threshold. This excitation provides a simple memory of the sensory stimulus. It allows temporal and spatial integration of sensory inputs and explains the long, variable delays to swimming. The process resembles the ‘accumulation’ of excitation proposed for cortical circuits in mammals. We conclude that fundamental elements of sensory memory and decision making are present in the brainstem at a surprisingly early stage in development

A Network Model of Local Field Potential Activity in Essential Tremor and the Impact of Deep Brain Stimulation

Essential tremor (ET), a movement disorder characterised by an uncontrollable shaking of the affected body part, is often professed to be the most common movement disorder, affecting up to one percent of adults over 40 years of age. The precise cause of ET is unknown, however pathological oscillations of a network of a number of brain regions are implicated in leading to the disorder. Deep brain stimulation (DBS) is a clinical therapy used to alleviate the symptoms of a number of movement disorders. DBS involves the surgical implantation of electrodes into specific nuclei in the brain. For ET the targeted region is the ventralis intermedius (Vim) nucleus of the thalamus. Though DBS is effective for treating ET, the mechanism through which the therapeutic effect is obtained is not understood. To elucidate the mechanism underlying the pathological network activity and the effect of DBS on such activity, we take a computational modelling approach combined with electrophysiological data. The pathological brain activity was recorded intra-operatively via implanted DBS electrodes, whilst simultaneously recording muscle activity of the affected limbs. We modelled the network hypothesised to underlie ET using the Wilson-Cowan approach. The modelled network exhibited oscillatory behaviour within the tremor frequency range, as did our electrophysiological data. By applying a DBS-like input we suppressed these oscillations. This study shows that the dynamics of the ET network support oscillations at the tremor frequency and the application of a DBS-like input disrupts this activity, which could be one mechanism underlying the therapeutic benefit

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong