K-complexes, spindles, and ERPs as impulse responses: unification via neural field theory

Developmental characteristics of visual evoked potentials to different stimulation in normal children

OBJECTIVE

To determine the developmental characteristics of flash visual evoked potentials (FVEP) and pattern-reversal visual evoked potentials (PVEP) of healthy children.

METHODS

The data were collected with a Keypoint Workstation 9033A07; 168 children (2 months-13 years) were tested with FVEP and 101 (4-13 years) were tested with PVEP.

RESULTS

A triphasic waveform with clear components (N2, P2, and N3) was recorded steadily after 1 year, with occurrence rates over 97% at all frequencies. FVEP latency significantly decreased with age. The amplitude difference of FVEP was greater for binocular than monocular fields. FVEP amplitude increased and amplitude differences decreased with stimulation frequency. The occurrence rate of PVEP was 100% after 4 years, and PVEP latency was significantly prolonged with age. N75 and P100 amplitudes and the N75-P100 amplitude difference increased with field of vision.

CONCLUSION

FVEP can be evoked in normal children at less than 2 Hz. Stimulation frequency can be adjusted to improve early detection and verification of subclinical lesions. The PVEP waveform is simple and stable, and its results are easier to analyze and interpret than FVEP, but it is limited by visual acuity and fixation force, whereas FVEP is affected less by visual acuity. but it is necessary to establish normal reference values of each age in each laboratory because of complicated analysis. According to the specific situation of the patient (vision, fixation) and clinical demand, we need to choose the right stimulation.

Evoked response activity eigenmode analysis in a convoluted cortex via neural field theory

Neural field theory of the corticothalamic system is used to explore evoked response potentials (ERPs) caused by spatially localized impulse stimuli on the convoluted cortex and on a spherical cortex. Eigenfunctions are calculated analytically on the spherical cortex and numerically on the convoluted cortex via eigenfunction expansions. Eigenmodes on a convoluted cortex are similar to those of the spherical cortex, and a few such modes are found to be sufficient to reproduce the main ERP features. It is found that the ERP peak is stronger in spherical cortex than convoluted cortex, but in both cases the peak decreases monotonically with increasing distance from the stimulus point. In the convoluted case, cortical folding causes ERPs to differ between locations at the same distance from the stimulus point and spherical symmetries are only approximately preserved.

Modal-Polar Representation of Evoked Response Potentials in Multiple Arousal States

An expansion of the corticothalamic transfer function into eigenmodes and resonant poles is used to derive a simple formula for evoked response potentials (ERPs) in various states of arousal. The transfer function corresponds to the cortical response to an external stimulus, which encodes all the information and properties of the linear system. This approach links experimental observations of resonances and characteristic timescales in brain activity with physically based neural field theory (NFT). The present work greatly simplifies the formula of the analytical ERP, and separates its spatial part (eigenmodes) from the temporal part (poles). Within this framework, calculations involve contour integrations that yield an explicit expression for ERPs. The dominant global mode is considered explicitly in more detail to study how the ERP varies with time in this mode and to illustrate the method. For each arousal state in sleep and wake, the resonances of the system are determined and it is found that five poles are sufficient to study the main dynamics of the system in waking eyes-open and eyes-closed states. Similarly, it is shown that six poles suffice to reproduce ERPs in rapid-eye movement sleep, sleep state 1, and sleep state 2 states, whereas just four poles suffice to reproduce the dynamics in slow wave sleep. Thus, six poles are sufficient to preserve the main global ERP dynamics of the system for all states of arousal. These six poles correspond to the dominant resonances of the system at slow-wave, alpha, and beta frequencies. These results provide the basis for simplified analytic treatment of brain dynamics and link observations more closely to theory.

Neural field theory of evoked response potentials in a spherical brain geometry

Evoked response potentials (ERPs) are calculated in spherical and planar geometries using neural field theory of the corticothalamic system. The ERP is modeled as an impulse response and the resulting modal effects of spherical corticothalamic dynamics are explored, showing that results for spherical and planar geometries converge in the limit of large brain size. Cortical modal effects can lead to a double-peak structure in the ERP time series. It is found that the main difference between infinite planar geometry and spherical geometry is that the ERP peak is sharper and stronger in the spherical geometry. It is also found that the magnitude of the response decreases with increasing spatial width of the stimulus at the cortex. The peak is slightly delayed at large angles from the stimulus point, corresponding to group velocities of 6-10 m s^{-1}. Strong modal effects are found in the spherical geometry, with the lowest few modes sufficing to describe the main features of ERPs, except very near to spatially narrow stimuli.

Physiology-based ERPs in normal and abnormal states

Evoked response potentials (ERPs) and other transients are modeled as impulse responses using physiology-based neural field theory (NFT) of the corticothalamic system of neural activity in the human brain that incorporates synaptic and dendritic dynamics, firing response, axonal propagation, and corticocortical and corticothalamic pathways. The properties of model-predicted ERPs are explored throughout the stability zone of the corticothalamic system, and predicted time series and wavelet spectra are also analyzed. This provides a unified treatment of predicted ERPs for both normal and abnormal states within the brain's stability zone, including likely parameters to represent abnormal states of reduced arousal.

Optimization by Adaptive Stochastic Descent

When standard optimization methods fail to find a satisfactory solution for a parameter fitting problem, a tempting recourse is to adjust parameters manually. While tedious, this approach can be surprisingly powerful in terms of achieving optimal or near-optimal solutions. This paper outlines an optimization algorithm, Adaptive Stochastic Descent (ASD), that has been designed to replicate the essential aspects of manual parameter fitting in an automated way. Specifically, ASD uses simple principles to form probabilistic assumptions about (a) which parameters have the greatest effect on the objective function, and (b) optimal step sizes for each parameter. We show that for a certain class of optimization problems (namely, those with a moderate to large number of scalar parameter dimensions, especially if some dimensions are more important than others), ASD is capable of minimizing the objective function with far fewer function evaluations than classic optimization methods, such as the Nelder-Mead nonlinear simplex, Levenberg-Marquardt gradient descent, simulated annealing, and genetic algorithms. As a case study, we show that ASD outperforms standard algorithms when used to determine how resources should be allocated in order to minimize new HIV infections in Swaziland.