Spatiotemporally varying visual hallucinations: II. Spectral classification and comparison with theory.

In order to better understand the nature of visual hallucinations, and to test predictions of spatiotemporally oscillating hallucinations from a recent corticothalamic model of visual dynamics, clinical descriptions of hallucinations are used to establish boundaries on the spatiotemporal frequencies observed in various disorders. Detailed comparisons with hallucinations during migraine aura demonstrate that key features are consistent with corticothalamic origin and specific abnormalities, but underline the need for more detailed quantitative data to be obtained on temporally oscillating hallucinations more generally.

Spatiotemporally varying visual hallucinations: I. Corticothalamic theory.

The thalamus is introduced to a recent model of the visual cortex to examine its effect on pattern formation in general and the generation of temporally oscillating patterns in particular. By successively adding more physiological details to a basic corticothalamic model, it is determined which features are responsible for which effects. In particular, with the addition of a thalamic population, several changes occur in the spatiotemporal power spectrum: power increases at resonances of the corticothalamic loop, while the loop acts as a spatiotemporal low-pass filter, and synaptic and dendritic dynamics temporally low-pass filter the activity more generally. Investigation of the effect of altering parameters and gains reveals new parameter regimes where activity that corresponds to hallucinations is induced by both spatially homogeneous and inhomogeneous temporally oscillating modes. This suggests that the thalamus and corticothalamic loops are essential components of a model of oscillating visual hallucinations.

Spatiotemporal hemodynamic response functions derived from physiology.

Probing neural activity with functional magnetic resonance imaging (fMRI) relies upon understanding the hemodynamic response to changes in neural activity. Although existing studies have extensively characterized the temporal hemodynamic response, less is understood about the spatial and spatiotemporal hemodynamic responses. This study systematically characterizes the spatiotemporal response by deriving the hemodynamic response due to a short localized neural drive, i.e., the spatiotemporal hemodynamic response function (stHRF) from a physiological model of hemodynamics based on a poroelastic model of cortical tissue. In this study, the model's boundary conditions are clarified and a resulting nonlinear hemodynamic wave equation is derived. From this wave equation, damped linear hemodynamic waves are predicted from the stHRF. The main features of these waves depend on two physiological parameters: wave propagation speed, which depends on mean cortical stiffness, and damping which depends on effective viscosity. Some of these predictions were applied and validated in a companion study (Aquino et al., 2012). The advantages of having such a theory for the stHRF include improving the interpretation of spatiotemporal dynamics in fMRI data; improving estimates of neural activity with fMRI spatiotemporal deconvolution; and enabling wave interactions between hemodynamic waves to be predicted and exploited to improve the signal to noise ratio of fMRI.

Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model.

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal, including both spatial and temporal dynamics for the first time. The brain tissue is modeled as a porous elastic medium, whose interconnected pores represent the vasculature. The model explicitly incorporates conservation of blood mass, interconversion of oxygenated and deoxygenated hemoglobin, force balance within the blood and of blood pressure with vessel walls, and blood flow modulation due to neuronal activity. In appropriate limits it is shown to reproduce prior Balloon models of hemodynamic response, which do not include spatial variations. The regime of validity of such models is thereby clarified by elucidating their assumptions, and when these break down, for example when voxel sizes become small.

Spatiotemporal dynamics of pattern formation in the primary visual cortex and hallucinations.

The existence of visual hallucinations with prominent temporal oscillations is well documented in conditions such as Charles Bonnett Syndrome. To explore these phenomena, a continuum model of cortical activity that includes additional physiological features of axonal propagation and synapto-dendritic time constants, is used to study the generation of hallucinations featuring both temporal and spatial oscillations. A detailed comparison of the physiological features of this model with those of two others used previously in the modeling of hallucinations is made, and differences, particularly regarding temporal dynamics, relevant to pattern formation are analyzed. Linear analysis and numerical calculation are then employed to examine the pattern forming behavior of this new model for two different forms of spatiotemporal coupling between neurons. Numerical calculations reveal an oscillating mode whose frequency depends on synaptic, dendritic, and axonal time constants not previously simultaneously included in such analyses. Its properties are qualitatively consistent with descriptions of a number of physiological disorders and conditions with temporal dynamics, but the analysis implies that corticothalamic effects will need to be incorporated to treat the consequences quantitatively.

Firing pattern of bursting neurons under sinusoidal drive in mean-field modeling.

Bursting has been observed in many sensory neurons, and is thought to be important in neural signaling, sleep, and some disorders of the brain. Bursting neurons have been studied via various types of conductance-based models at the single-neuron level. Important features of bursting have been reproduced by this type of model, but it is not certain how well the behavior of populations of bursting neurons can be represented solely by that of individual neurons. To study bursting neurons at the population level, a conductance-based model is incorporated into a mean-field model to yield a mean-field bursting model. The responses of the model to sinusoidal inputs are studied, showing that neurons with various different initial states are capable of phase-locked or intermittent firing, depending on their baseline voltage. Furthermore, depending on this voltage, the bursting frequency either slaves to the original unperturbed bursting frequency or approaches a steady value when the external driving frequency increases. Finally, use of white noise perturbations shows that the bursting frequency of the neurons remains the same even under a more general external stimulus.

Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations.

Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker intracortical connections in parkinsonian patients. Strict separation of the direct and indirect pathways is not necessary to obtain these results.

BOLD responses to stimuli: dependence on frequency, stimulus form, amplitude, and repetition rate.

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level-dependent (BOLD) functional MRI signal. The relationship of stimuli to neuronal activity during evoked responses is inferred from recent physiology-based quantitative modeling of evoked response potentials (ERPs). A hemodynamic model is then used to calculate the BOLD response to neuronal activity having the form of an impulse, a sinusoid, or an ERP-like damped sinusoid. Using the resulting equations, the BOLD response is analyzed for different forms, frequencies, and amplitudes of stimuli, in contrast with previous research, which has mostly concentrated on sustained stimuli. The BOLD frequency response is found to be closely linear in the parameter ranges of interest, with the form of a low-pass filter with a weak resonance at approximately 0.07 Hz. An improved BOLD impulse response is systematically obtained which includes initial dip and post-stimulus undershoot for some parameter ranges. It is found that the BOLD response depends strongly on the precise temporal course of the evoked neuronal activity, not just its peak value or typical amplitude. Indeed, for short stimuli, the linear BOLD response is closely proportional to the time-integrated activity change evoked by the stimulus, regardless of amplitude. It is concluded that there can be widely differing proportionalities between BOLD and peak activity, that this is the likely reason for the low level of correspondence seen experimentally between ERP sources and BOLD measurements and that non-BOLD measurements, such as ERPs, can be used to correct for this effect to obtain improved activity estimates. Finally, stimulus sequences that optimize the signal-to-noise ratio in event-related BOLD fMRI (efMRI) experiments are derived using the hemodynamic transfer function.

Lévy walks in random scattering and growth of waves.

Random spatial wave scattering and stochastic wave growth are studied where one or both of the random processes can be described by a Lévy walk. This analysis extends previous work on randomly growing and scattering waves where both the random processes are modeled by Gaussian diffusive statistics. Both random spatial scattering and stochastic wave growth modeled by Lévy walks are studied separately, together, and in combination with Gaussian processes. Transmission coefficients, lasing thresholds, and energy densities in the medium are obtained for the different permutations.