Dimensional reduction of direct statistical simulation

Direct statistical simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by direct numerical simulation (DNS). That low-order statistics usually evolve slowly compared with instantaneous dynamics is one important advantage of DSS. Depending on the symmetry of the problem and the choice of averaging operation, however, DSS is usually more expensive computationally than DNS because even low-order statistics typically have higher dimension than the underlying fields. Here we show that it is in some cases possible to go much further by using a form of unsupervised learning, proper orthogonal decomposition, to address the ‘curse of dimensionality’. We apply proper orthogonal decomposition directly to DSS in the form of expansions in equal-time cumulants to second order. We explore two averaging operations (zonal and ensemble) and test the approach on two idealized barotropic models of fluid on a rotating sphere (a jet that relaxes deterministically towards an unstable profile and a stochastically driven flow that spontaneously organizes into jets). We show that the method offers the possibility of parameter continuation, in the reduced basis, for the lower-order statistics of the flow. Order-of-magnitude savings in computational cost are sometimes obtained in the reduced basis, potentially enabling access to parameter regimes beyond the reach of DNS

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Prefrontal Network Engagement by Deep Brain Stimulation in Limbic Hubs

Prefrontal circuits in the human brain play an important role in cognitive and affective processing. Neuromodulation therapies delivered to certain key hubs within these circuits are being used with increasing frequency to treat a host of neuropsychiatric disorders. However, the detailed neurophysiological effects of stimulation to these hubs are largely unknown. Here, we performed intracranial recordings across prefrontal networks while delivering electrical stimulation to two well-established white matter hubs involved in cognitive regulation and depression: the subcallosal cingulate (SCC) and ventral capsule/ventral striatum (VC/VS). We demonstrate a shared frontotemporal circuit consisting of the ventromedial prefrontal cortex, amygdala, and lateral orbitofrontal cortex where gamma oscillations are differentially modulated by stimulation target. Additionally, we found participant-specific responses to stimulation in the dorsal anterior cingulate cortex and demonstrate the capacity for further tuning of neural activity using current-steered stimulation. Our findings indicate a potential neurophysiological mechanism for the dissociable therapeutic effects seen across the SCC and VC/VS targets for psychiatric neuromodulation and our results lay the groundwork for personalized, network-guided neurostimulation therapy

Stereo-Eeg-Guided Network Modulation for Psychiatric Disorders: Surgical Considerations

BACKGROUND: Deep brain stimulation (DBS) and other neuromodulatory techniques are being increasingly utilized to treat refractory neurologic and psychiatric disorders. OBJECTIVE: /Hypothesis: To better understand the circuit-level pathophysiology of treatment-resistant depression (TRD) and treat the network-level dysfunction inherent to this challenging disorder, we adopted an approach of inpatient intracranial monitoring borrowed from the epilepsy surgery field. METHODS: We implanted 3 patients with 4 DBS leads (bilateral pair in both the ventral capsule/ventral striatum and subcallosal cingulate) and 10 stereo-electroencephalography (sEEG) electrodes targeting depression-relevant network regions. For surgical planning, we used an interactive, holographic visualization platform to appreciate the 3D anatomy and connectivity. In the initial surgery, we placed the DBS leads and sEEG electrodes using robotic stereotaxy. Subjects were then admitted to an inpatient monitoring unit for depression-specific neurophysiological assessments. Following these investigations, subjects returned to the OR to remove the sEEG electrodes and internalize the DBS leads to implanted pulse generators. RESULTS: Intraoperative testing revealed positive valence responses in all 3 subjects that helped verify targeting. Given the importance of the network-based hypotheses we were testing, we required accurate adherence to the surgical plan (to engage DBS and sEEG targets) and stability of DBS lead rotational position (to ensure that stimulation field estimates of the directional leads used during inpatient monitoring were relevant chronically), both of which we confirmed (mean radial error 1.2±0.9 mm; mean rotation 3.6±2.6°). CONCLUSION: This novel hybrid sEEG-DBS approach allows detailed study of the neurophysiological substrates of complex neuropsychiatric disorders

The Case for Adaptive Neuromodulation to Treat Severe Intractable Mental Disorders

Mental disorders are a leading cause of disability worldwide, and available treatments have limited efficacy for severe cases unresponsive to conventional therapies. Neurosurgical interventions, such as lesioning procedures, have shown success in treating refractory cases of mental illness, but may have irreversible side effects. Neuromodulation therapies, specifically Deep Brain Stimulation (DBS), may offer similar therapeutic benefits using a reversible (explantable) and adjustable platform. Early DBS trials have been promising, however, pivotal clinical trials have failed to date. These failures may be attributed to targeting, patient selection, or the “open-loop” nature of DBS, where stimulation parameters are chosen ad hoc during infrequent visits to the clinician’s office that take place weeks to months apart. Further, the tonic continuous stimulation fails to address the dynamic nature of mental illness; symptoms often fluctuate over minutes to days. Additionally, stimulation-based interventions can cause undesirable effects if applied when not needed. A responsive, adaptive DBS (aDBS) system may improve efficacy by titrating stimulation parameters in response to neural signatures (i.e., biomarkers) related to symptoms and side effects. Here, we present rationale for the development of a responsive DBS system for treatment of refractory mental illness, detail a strategic approach for identification of electrophysiological and behavioral biomarkers of mental illness, and discuss opportunities for future technological developments that may harness aDBS to deliver improved therapy

Automated and rapid self-report of nociception in transgenic mice

AbstractA time-resolved, conscious report of detected nociceptive stimuli in mice offers an opportunity to examine the relationship between higher order neural circuits and pain perception. We have developed a detection behavior in transgenic mice that leverages temporally precise and cell-specific stimulation to elicit self-reports of nociception. Conscious reporting of peripheral nociceptive input may help identify neural mechanisms that generate pain perception.</jats:p