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.