Alzheimer's disease (AD) not only involves loss of memory functions, but also prominent deterioration of sleep physiology, which is already evident at the stage of mild cognitive impairment (MCI). Cortical slow oscillations (SO; 0.5-1 Hz) and thalamocortical spindle activity (12-15 Hz) during sleep, and their temporal coordination, are considered critical for memory formation. We investigated the potential of slow oscillatory transcranial direct current stimulation (so-tDCS), applied during a daytime nap in a sleep-state-dependent manner, to modulate these activity patterns and sleep-related memory consolidation in nine male and seven female human patients with MCI. Stimulation significantly increased overall SO and spindle power, amplified spindle power during SO up-phases, and led to stronger synchronization between SO and spindle power fluctuations in EEG recordings. Moreover, visual declarative memory was improved by so-tDCS compared with sham stimulation and was associated with stronger synchronization. These findings indicate a well-tolerated therapeutic approach for disordered sleep physiology and memory deficits in MCI patients and advance our understanding of offline memory consolidation. In the light of increasing evidence that sleep disruption is crucially involved in the progression of Alzheimer's disease (AD), sleep appears as a promising treatment target in this pathology, particularly to counteract memory decline. This study demonstrates the potential of a noninvasive brain stimulation method during sleep in patients with mild cognitive impairment (MCI), a precursor of AD, and advances our understanding of its mechanism. We provide first time evidence that slow oscillatory transcranial stimulation amplifies the functional cross-frequency coupling between memory-relevant brain oscillations and improves visual memory consolidation in patients with MCI.

Human lumbar spinal cord networks controlling stepping and standing can be activated through posterior root stimulation using implanted electrodes. A new stimulation method utilizing surface electrodes has been shown to excite lumbar posterior root fibers similarly as with implants, an unexpected finding considering the distance to these target neurons. In the present study we apply computer modeling to compare the depolarization of posterior root fibers by both stimulation techniques. We further examine the potential for additional direct activation of motoneurons within the anterior roots. Using an implant, action potentials are initiated in the posterior root fibers at their entry into the spinal cord or along the longitudinal portions of the fiber trajectories, depending on the cathode position. For transcutaneous stimulation low threshold sites of the same fibers are identified at their exits from the spinal canal in addition to their spinal cord entries. In these exit regions anterior root fibers can also be activated. The simulation results provide a biophysical explanation for the electrophysiological findings of lower limb muscle responses induced by posterior root stimulation. Efficient excitation of afferent spinal cord structures with a simple noninvasive method can become a promising modality in the rehabilitation of people with motor disorders.

Stimulation of different spinal cord segments in humans is a widely developed clinical practice for modification of pain, altered sensation and movement. The human lumbar cord has become a target for modification of motor control by epidural and more recently by transcutaneous spinal cord stimulation. Posterior columns of the lumbar spinal cord represent a vertical system of axons and when activated can add other inputs to the motor control of the spinal cord than stimulated posterior roots. We used a detailed three-dimensional volume conductor model of the torso and the McIntyre-Richard-Grill axon model to calculate the thresholds of axons within the posterior columns in response to transcutaneous lumbar spinal cord stimulation. Superficially located large diameter posterior column fibers with multiple collaterals have a threshold of 45.4 V, three times higher than posterior root fibers (14.1 V). With the stimulation strength needed to activate posterior column axons, posterior root fibers of large and small diameters as well as anterior root fibers are co-activated. The reported results inform on these threshold differences, when stimulation is applied to the posterior structures of the lumbar cord at intensities above the threshold of large-diameter posterior root fibers.

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

Neural mass signals from in-vivo recordings often show oscillations with frequencies ranging from <1 to 100 Hz. Fast rhythmic activity in the beta and gamma range can be generated by network-based mechanisms such as recurrent synaptic excitation-inhibition loops. Slower oscillations might instead depend on neuronal adaptation currents whose timescales range from tens of milliseconds to seconds. Here we investigate how the dynamics of such adaptation currents contribute to spike rate oscillations and resonance properties in recurrent networks of excitatory and inhibitory neurons. Based on a network of sparsely coupled spiking model neurons with two types of adaptation current and conductance-based synapses with heterogeneous strengths and delays we use a mean-field approach to analyze oscillatory network activity. For constant external input, we find that spike-triggered adaptation currents provide a mechanism to generate slow oscillations over a wide range of adaptation timescales as long as recurrent synaptic excitation is sufficiently strong. Faster rhythms occur when recurrent inhibition is slower than excitation and oscillation frequency increases with the strength of inhibition. Adaptation facilitates such network-based oscillations for fast synaptic inhibition and leads to decreased frequencies. For oscillatory external input, adaptation currents amplify a narrow band of frequencies and cause phase advances for low frequencies in addition to phase delays at higher frequencies. Our results therefore identify the different key roles of neuronal adaptation dynamics for rhythmogenesis and selective signal propagation in recurrent networks.

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.

Transcranial brain stimulation and evidence of ephaptic coupling have recently sparked strong interests in understanding the effects of weak electric fields on the dynamics of brain networks and of coupled populations of neurons. The collective dynamics of large neuronal populations can be efficiently studied using single-compartment (point) model neurons of the integrate-and-fire (IF) type as their elements. These models, however, lack the dendritic morphology required to biophysically describe the effect of an extracellular electric field on the neuronal membrane voltage. Here, we extend the IF point neuron models to accurately reflect morphology dependent electric field effects extracted from a canonical spatial “ball-and-stick” (BS) neuron model. Even in the absence of an extracellular field, neuronal morphology by itself strongly affects the cellular response properties. We, therefore, derive additional components for leaky and nonlinear IF neuron models to reproduce the subthreshold voltage and spiking dynamics of the BS model exposed to both fluctuating somatic and dendritic inputs and an extracellular electric field. We show that an oscillatory electric field causes spike rate resonance, or equivalently, pronounced spike to field coherence. Its resonance frequency depends on the location of the synaptic background inputs. For somatic inputs the resonance appears in the beta and gamma frequency range, whereas for distal dendritic inputs it is shifted to even higher frequencies. Irrespective of an external electric field, the presence of a dendritic cable attenuates the subthreshold response at the soma to slowly-varying somatic inputs while implementing a low-pass filter for distal dendritic inputs. Our point neuron model extension is straightforward to implement and is computationally much more efficient compared to the original BS model. It is well suited for studying the dynamics of large populations of neurons with heterogeneous dendritic morphology with (and without) the influence of weak external electric fields.

Many types of neurons exhibit spike rate adaptation, mediated by intrinsic slow K(+) currents, which effectively inhibit neuronal responses. How these adaptation currents change the relationship between in vivo like fluctuating synaptic input, spike rate output, and the spike train statistics, however, is not well understood. In this computational study we show that an adaptation current that primarily depends on the subthreshold membrane voltage changes the neuronal input-output relationship (I-O curve) subtractively, thereby increasing the response threshold, and decreases its slope (response gain) for low spike rates. A spike-dependent adaptation current alters the I-O curve divisively, thus reducing the response gain. Both types of an adaptation current naturally increase the mean interspike interval (ISI), but they can affect ISI variability in opposite ways. A subthreshold current always causes an increase of variability while a spike-triggered current decreases high variability caused by fluctuation-dominated inputs and increases low variability when the average input is large. The effects on I-O curves match those caused by synaptic inhibition in networks with asynchronous irregular activity, for which we find subtractive and divisive changes caused by external and recurrent inhibition, respectively. Synaptic inhibition, however, always increases the ISI variability. We analytically derive expressions for the I-O curve and ISI variability, which demonstrate the robustness of our results. Furthermore, we show how the biophysical parameters of slow K(+) conductances contribute to the two different types of an adaptation current and find that Ca(2+)-activated K(+) currents are effectively captured by a simple spike-dependent description, while muscarine-sensitive or Na(+)-activated K(+) currents show a dominant subthreshold component.