Per Danzl

A broadband vibrational energy harvester

We propose a design for an energy harvester which has the potential to harvest vibrational energy over a broad range of ambient frequencies. The device uses two flexible ceramic piezoelectric elements arranged in a buckled configuration in the absence of vibrations. Experimental data show that this design allows enhanced harvesting of energy relative to a comparable cantilever design, both for periodic and stochastic vibrations. Moreover, the data suggest that this harvester has its peak energy generation when it responds with chaotic vibrations.

Event-based minimum-time control of oscillatory neuron models: Phase randomization, maximal spike rate increase, and desynchronization

We present an event-based feedback control method for randomizing the asymptotic phase of oscillatory neurons. Phase randomization is achieved by driving the neuron’s state to its phaseless set, a point at which its phase is undefined and is extremely sensitive to background noise. We consider the biologically relevant case of a fixed magnitude constraint on the stimulus signal, and show how the control objective can be accomplished in minimum time. The control synthesis problem is addressed using the minimum-time-optimal Hamilton–Jacobi–Bellman framework, which is quite general and can be applied to any spiking neuron model in the conductance-based Hodgkin–Huxley formalism. We also use this methodology to compute a feedback control protocol for optimal spike rate increase. This framework provides a straightforward means of visualizing isochrons, without actually calculating them in the traditional way. Finally, we present an extension of the phase randomizing control scheme that is applied at the population level, to a network of globally coupled neurons that are firing in synchrony. The applied control signal desynchronizes the population in a demand-controlled way.

Spike timing control of oscillatory neuron models using impulsive and quasi-impulsive charge-balanced inputs

We propose a method to control the spike timing of a Type II oscillatory neuron to match the phase of a given reference oscillator. The control method is inspired by the impulsive character of neural communication in nature, and leads to a simple mathematical solution. We show that the phase response curve, which describes the phase-shift of the oscillation due to an impulsive perturbation as a function of the phase at which the perturbation occurs, contains sufficient information to design a charge-balanced control law that provides global monotonic convergence of oscillator phase to the reference phase. This feedback law requires only the knowledge of the dynamics gained through the phase reduction, and the ability to detect a once-per-period marker event, such as the time at which a neuron fires. The effectiveness of this control law is demonstrated through analytical and numerical results, including application to the full-dimensional conductance-based neuron model from which the phase-reduced model was derived. This work represents a step toward a closed-loop form of electrical deep brain stimulation, a treatment for neuromotor disorders such as Parkinsons disease, with symptoms characterized by pathologically synchronized neural firing.

Partial phase synchronization of neural populations due to random Poisson inputs.

We show that populations of identical uncoupled neurons exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. We characterize this partial synchronization using the phase distribution of the population, and consider analytical approximations and numerical simulations of phase-reduced models and the corresponding conductance-based models of typical Type I (Hindmarsh–Rose) and Type II (Hodgkin–Huxley) neurons, showing quantitatively how the extent of the partial phase synchronization depends on the magnitude and mean interspike frequency of the stimulus. Furthermore, we present several simple examples that disprove the notion that phase synchrony must be strongly related to spike synchrony. Instead, the importance of partial phase synchrony is shown to lie in its influence on the response of the population to stimulation, which we illustrate using first spike time histograms.

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.

Event-based feedback control of nonlinear oscillators using phase response curves

The phase response curve for a nonlinear oscillator describes the phase-shift of the oscillation due to an impulsive perturbation as a function of the phase at which the perturbation occurs. We propose a novel feedback control mechanism which allows one to control the phase of an oscillation, assuming only that the phase response curve is known and that a once-per-period marker event, such as the time at which a neuron fires, can be detected. The effectiveness of this control method is demonstrated through analytical and numerical results. This work represents a first step toward a closed-loop form of electrical deep brain stimulation, a treatment for neuromotor disorders such as Parkinsons disease, with symptoms characterized by pathological neural synchronization.

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.

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.