Tyler Stigen

Reconstructing micrometer-scale fiber pathways in the brain: Multi-contrast optical coherence tomography based tractography

Comprehensive understanding of connective neural pathways in the brain has put great challenges on the current imaging techniques, for which three-dimensional (3D) visualization of fiber tracts with high spatiotemporal resolution is desirable. Here we present optical imaging and tractography of rat brain ex-vivo using multi-contrast optical coherence tomography (MC-OCT), which is capable of simultaneously generating depth-resolved images of reflectivity, phase retardance, optic axis orientation and, for in-vivo studies, blood flow images. Using the birefringence property of myelin sheath, nerve fiber tracts as small as a few tens of micrometers can be resolved and neighboring fiber tracts with different orientations can be distinguished in cross-sectional optical slices, 2D en-face images and 3D volumetric images. Combinational contrast of MC-OCT images enables visualization of the spatial architecture and nerve fiber orientations in the brain with unprecedented detail. The results suggest that optical tractography, by virtue of its direct accessibility to nerve fibers, has the potential to validate diffusion magnetic resonance images and investigate structural connections in normal brain and neurological disorders. In addition, an endoscopic MC-OCT may be useful in neurosurgical interventions to aid in placement of deep brain stimulating electrodes.

Minimum energy control for in vitro neurons

OBJECTIVE To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats. APPROACH The method of control uses the phase model of a neuron and does not require prior knowledge of the neurons biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neurons phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential. MAIN RESULT The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli. SIGNIFICANCE The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments.

Controlling spike timing and synchrony in oscillatory neurons

We describe an algorithm to control synchrony between two periodically firing neurons. The control scheme operates in real-time using a dynamic clamp platform. This algorithm is a low-impact stimulation method that brings the neurons toward the desired level of synchrony over the course of several neuron firing periods. As a proof of principle, we demonstrate the versatility of the algorithm using real-time conductance models and then show its performance with biological neurons of hippocampal region CA1 and entorhinal cortex.

Nanowires precisely grown on the ends of microwire electrodes permit the recording of intracellular action potentials within deeper neural structures.

AIMS Nanoelectrodes are an emerging biomedical technology that can be used to record intracellular membrane potentials from neurons while causing minimal damage during membrane penetration. Current nanoelectrode designs, however, have low aspect ratios or large substrates and thus are not suitable for recording from neurons deep within complex natural structures, such as brain slices. MATERIALS & METHODS We describe a novel nanoelectrode design that uses nanowires grown on the ends of microwire recording electrodes similar to those frequently used in vivo. RESULTS & DISCUSSION We demonstrate that these nanowires can record intracellular action potentials in a rat brain slice preparation and in isolated leech ganglia. CONCLUSION Nanoelectrodes have the potential to revolutionize intracellular recording methods in complex neural tissues, to enable new multielectrode array technologies and, ultimately, to be used to record intracellular signals in vivo.

Single neuron dynamics during experimentally induced anoxic depolarization.

We studied single neuron dynamics during anoxic depolarizations, which are often observed in cases of neuronal energy depletion. Anoxic and similar depolarizations play an important role in several pathologies, notably stroke, migraine, and epilepsy. One of the effects of energy depletion was experimentally simulated in slices of rat cortex by blocking the sodium-potassium pumps with ouabain. The membrane voltage of pyramidal cells was measured. Five different kinds of dynamical behavior of the membrane voltage were observed during the resulting depolarizations. Using bifurcation analysis of a single cell model, we show that these voltage dynamics all are responses of the same cell, with normally functioning ion channels, to particular courses of the intra- and extracellular concentrations of sodium and potassium.

Linear control of neuronal spike timing using phase response curves

We propose a simple, robust, linear method to control the spike timing of a periodically firing neuron. The control scheme uses the neuron’s phase response curve to identify an area of optimal sensitivity for the chosen stimulation parameters. The spike advance as a function of current pulse amplitude is characterized at the optimal phase and a linear least-squares regression is fit to the data. The inverted regression is used as the control function for this method. The efficacy of this method is demonstrated through numerical simulations of a Hodgkin-Huxley style neuron model as well as in real neurons from rat hippocampal slice preparations. The study shows a proof of concept for the application of a linear control scheme to control neuron spike timing in-vitro. This study was done on an individual cell level, but translation to a tissue or network level is possible. Control schemes of this type could be implemented in a closed loop implantable device to treat neuromotor disorders involving pathologically neuronal activity such as epilepsy or Parkinson’s disease.

Corrigendum: Minimum energy control for in vitro neurons

Objective. To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats. Approach. The method of control uses the phase model of a neuron and does not require prior knowledge of the neuron’s biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neuron’s phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential. Main result. The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli. Significance. The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments. (Some figures may appear in colour only in the online journal)

Linear Control of Neuronal Spike Timing Using Phase Response Curves

We propose a simple, robust, and linear method to control the spike timing of a periodically firing neuron. The control scheme uses the neuron’s phase response curve to identify an area of optimal sensitivity for the chosen stimulation parameters. The spike advance as a function of current pulse amplitude is characterized at the optimal phase, and a linear least-squares regression is fit to the data. The inverted regression is used as the control function for this method. The efficacy of this method is demonstrated through numerical simulations of a Hodgkin–Huxley style neuron model as well as in real neurons from rat hippocampal slice preparations. The study shows a proof of concept for the application of a linear control scheme to control neuron spike timing in vitro. This study was done on an individual cell level, but translation to a tissue or network level is possible. Control schemes of this type could be implemented in a closed loop implantable device to treat neuromotor disorders involving pathologically neuronal activity such as epilepsy or Parkinson’s disease.

Designing anti-epileptic drugs using neuronal dynamics

While the molecular mechanism of many anti-epileptic drugs (AEDs) is known, rational drug design for anti-epileptic drugs has been hindered by our lack of understanding on how these mechanisms influence system level behaviors. Using phase reduction techniques, we can relate molecular level changes to network level synchrony to understand how a drug may influence system level behavior. After studying the effect of AEDs on neuronal dynamics using both electrophysiology and computational models, we observed a reduction in firing rate and minor changes in the phase response curve (PRC) to synaptic inputs. This finding was common among drugs with completely different mechanisms of action: phenytoin (voltage gated Na+ blocker), ethosuximide (T-type Ca++ blocker), and retigabine (voltage gated K+ opener). When controlling for firing rate, we found no significant changes to the PRC of the neuron. The PRC relates the synaptic input to the spike time output of a neuron, it is logical that preservation of those dynamics is critical to the functional information processing in the system. This led us to hypothesize that the best AEDs may reduce the firing rate of the neuron while preserving the PRC. The slower firing rate reduces neurotransmitter release and synaptic summation, thus reducing activity in a population while maintaining the essential information transfer characteristics of the neuron. This hypothesis was tested in a computational neuron model [1], which has 6 currents and 36 parameters. A subset of parameters was examined, excluding those which would remain relatively static in a biological neuron. Each of the 24 qualifying parameters was altered until a 5 ms increase in the interspike interval was achieved compared to the control interspike interval (100 ms). We then measured the phase response curve and compared the sum squared error (SSE) relative to the control. Ranking the SSE of the PRC (Table ​(Table1)1) for each parameter showed that target of the known convulsant drug, 4-aminopyridine, had the greatest error in the phase response curve (156.3), while the known AED phenytoin showed lower error (115.9). Additionally, the highest ranking parameters (those which best preserve the PRC) were all K+ currents that do not currently have a corresponding AED. Drugs targeting those parameters which best preserve the PRC while reducing firing rate may prove to be effective AEDs according to the hypothesis presented here. This technique is easily extensible to the addition of any channel and error rankings of the 24 parameters remained consistent across different firing rates. This method may provide a principled approach for determining which drug targets will be effective for the treatment of epilepsy and illustrate how neuronal dynamics can give us the information needed to understand system level effects related to molecular level drug mechanics, thus allowing us to engineer better medicine. Table 1 Predicted Effectiveness of AED Target