Schizophrenia—a parameters’ game?

A mathematical model of reward and executive circuitry in obsessive compulsive disorder

The neuronal circuit that controls obsessive and compulsive behaviors involves a complex network of brain regions (some with known involvement in reward processing). Among these are cortical regions, the striatum and the thalamus (which compose the CSTC pathway), limbic areas such as the amygdala and the hippocampus, as well as dopamine pathways. Abnormal dynamic behavior in this brain network is a hallmark feature of patients with increased anxiety and motor activity, like the ones affected by OCD. There is currently no clear understanding of precisely what mechanisms generate these behaviors. We attempt to investigate a collection of connectivity hypotheses of OCD by means of a computational model of the brain circuitry that governs reward and motion execution. Mathematically, we use methods from ordinary differential equations and continuous time dynamical systems. We use classical analytical methods as well as computational approaches to study phenomena in the phase plane (e.g., behavior of the system's solutions when given certain initial conditions) and in the parameter space (e.g., sensitive dependence of initial conditions). We find that different obsessive-compulsive subtypes may correspond to different abnormalities in the network connectivity profiles. We suggest that it is a combination of parameters (connectivity strengths between regions), rather than the value of any one parameter taken independently, that provide the best basis for predicting behavior, and for understanding the heterogeneity of the illness.

Emotion: The Self-regulatory Sense

While emotion is a central component of human health and well-being, traditional approaches to understanding its biological function have been wanting. A dynamic systems model, however, broadly redefines and recasts emotion as a primary sensory system-perhaps the first sensory system to have emerged, serving the ancient autopoietic function of "self-regulation." Drawing upon molecular biology and revelations from the field of epigenetics, the model suggests that human emotional perceptions provide an ongoing stream of "self-relevant" sensory information concerning optimally adaptive states between the organism and its immediate environment, along with coupled behavioral corrections that honor a universal self-regulatory logic, one still encoded within cellular signaling and immune functions. Exemplified by the fundamental molecular circuitry of sensorimotor control in the E coli bacterium, the model suggests that the hedonic (affective) categories emerge directly from positive and negative feedback processes, their good/bad binary appraisals relating to dual self-regulatory behavioral regimes-evolutionary purposes, through which organisms actively participate in natural selection, and through which humans can interpret optimal or deficit states of balanced being and becoming. The self-regulatory sensory paradigm transcends anthropomorphism, unites divergent theoretical perspectives and isolated bodies of literature, while challenging time-honored assumptions. While suppressive regulatory strategies abound, it suggests that emotions are better understood as regulating us, providing a service crucial to all semantic language, learning systems, evaluative decision-making, and fundamental to optimal physical, mental, and social health.

Network connectivity modulates power spectrum scale invariance

Measures of complexity are sensitive in detecting disease, which has made them attractive candidates for diagnostic biomarkers; one complexity measure that has shown promise in fMRI is power spectrum scale invariance (PSSI). Even if scale-free features of neuroimaging turn out to be diagnostically useful, however, their underlying neurobiological basis is poorly understood. Using modeling and simulations of a schematic prefrontal-limbic meso-circuit, with excitatory and inhibitory networks of nodes, we present here a framework for how network density within a control system can affect the complexity of signal outputs. Our model demonstrates that scale-free behavior, similar to that observed in fMRI PSSI data, can be obtained for sufficiently large networks in a context as simple as a linear stochastic system of differential equations, although the scale-free range improves when introducing more realistic, nonlinear behavior in the system. PSSI values (reflective of complexity) vary as a function of both input type (excitatory, inhibitory) and input density (mean number of long-range connections, or strength), independent of their node-specific geometric distribution. Signals show pink noise (1/f) behavior when excitatory and inhibitory influences are balanced. As excitatory inputs are increased and decreased, signals shift towards white and brown noise, respectively. As inhibitory inputs are increased and decreased, signals shift towards brown and white noise, respectively. The results hold qualitatively at the hemodynamic scale, which we modeled by introducing a neurovascular component. Comparing hemodynamic simulation results to fMRI PSSI results from 96 individuals across a wide spectrum of anxiety-levels, we show how our model can generate concrete and testable hypotheses for understanding how connectivity affects regulation of meso-circuits in the brain.

Power spectrum scale invariance identifies prefrontal dysregulation in paranoid schizophrenia

Theory and experimental evidence suggest that complex living systems function close to the boundary of chaos, with erroneous organization to an improper dynamical range (too stiff or chaotic) underlying system-wide dysregulation and disease. We hypothesized that erroneous organization might therefore also characterize paranoid schizophrenia, via optimization abnormalities in the prefrontal-limbic circuit regulating emotion. To test this, we acquired fMRI scans from 35 subjects (N = 9 patients with paranoid schizophrenia and N = 26 healthy controls), while they viewed affect-valent stimuli. To quantify dynamic regulation, we analyzed the power spectrum scale invariance (PSSI) of fMRI time-courses and computed the geometry of time-delay (Poincaré) maps, a measure of variability. Patients and controls showed distinct PSSI in two clusters (k(1) : Z = 4.3215, P = 0.00002 and k(2) : Z = 3.9441, P = 0.00008), localized to the orbitofrontal/medial prefrontal cortex (Brodmann Area 10), represented by β close to white noise in patients (β ≈ 0) and in the pink noise range in controls (β ≈ -1). Interpreting the meaning of PSSI differences, the Poincaré maps indicated less variability in patients than controls (Z = -1.9437, P = 0.05 for k(1) ; Z = -2.5099, P = 0.01 for k(2) ). That the dynamics identified Brodmann Area 10 is consistent with previous schizophrenia research, which implicates this area in deficits of working memory, executive functioning, emotional regulation and underlying biological abnormalities in synaptic (glutamatergic) transmission. Our results additionally cohere with a large body of work finding pink noise to be the normal range of central function at the synaptic, cellular, and small network levels, and suggest that patients show less supple responsivity of this region.

A principal component network analysis of prefrontal-limbic functional magnetic resonance imaging time series in schizophrenia patients and healthy controls

We investigated neural regulation of emotional arousal. We hypothesized that the interactions between the components of the prefrontal-limbic system determine the global trajectories of the individual's brain activation, with the strengths and modulations of these interactions being potentially key components underlying the differences between healthy individuals and those with schizophrenia. Using affect-valent facial stimuli presented to 11 medicated schizophrenia patients and 65 healthy controls, we activated neural regions associated with the emotional arousal response during functional magnetic resonance imaging (fMRI). Performing first a random effects analysis of the fMRI data to identify activated regions, we obtained 352 data-point time series for six brain regions: bilateral amygdala, hippocampus and two prefrontal regions (Brodmann Areas 9 and 45). Since standard statistical methods are not designed to capture system features and evolution, we used principal component analyses on two types of pre-processed data: contrasts and group averages. We captured an important characteristic of the evolution of our six-dimensional brain network: all subject trajectories are almost embedded in a two-dimensional plane. Moreover, the direction of the largest principal component was a significant differentiator between the control and patient populations: the left and right amygdala coefficients were substantially higher in the case of patients, and the coefficients of Brodmann Area 9 were, to a lesser extent, higher in controls. These results are evidence that modulations between the regions of interest are the important determinant factors for the system's dynamical behavior. We place our results within the context of other principal component analyses used in neuroimaging, as well as of our existing theoretical model of prefrontal-limbic dysregulation.