Towards dynamical network biomarkers in neuromodulation of episodic migraine

Spontaneous transitions to focal-onset epileptic seizures: A dynamical study

Given the complex temporal evolution of epileptic seizures, understanding their dynamic nature might be beneficial for clinical diagnosis and treatment. Yet, the mechanisms behind, for instance, the onset of seizures are still unknown. According to an existing classification, two basic types of dynamic onset patterns plus a number of more complex onset waveforms can be distinguished. Here, we introduce a basic three-variable model with two time scales to study potential mechanisms of spontaneous seizure onset. We expand the model to demonstrate how coupling of oscillators leads to more complex seizure onset waveforms. Finally, we test the response to pulse perturbation as a potential biomarker of interictal changes.

Leptin and Associated Mediators of Immunometabolic Signaling: Novel Molecular Outcome Measures for Neurostimulation to Treat Chronic Pain

Chronic pain is a devastating condition affecting the physical, psychological, and socioeconomic status of the patient. Inflammation and immunometabolism play roles in the pathophysiology of chronic pain disorders. Electrical neuromodulation approaches have shown a meaningful success in otherwise drug-resistant chronic pain conditions, including failed back surgery, neuropathic pain, and migraine. A literature review (PubMed, MEDLINE/OVID, SCOPUS, and manual searches of the bibliographies of known primary and review articles) was performed using the following search terms: chronic pain disorders, systemic inflammation, immunometabolism, prediction, biomarkers, metabolic disorders, and neuromodulation for chronic pain. Experimental studies indicate a relationship between the development and maintenance of chronic pain conditions and a deteriorated immunometabolic state mediated by circulating cytokines, chemokines, and cellular components. A few uncontrolled in-human studies found increased levels of pro-inflammatory cytokines known to drive metabolic disorders in chronic pain patients undergoing neurostimulation therapies. In this narrative review, we summarize the current knowledge and possible relationships of available neurostimulation therapies for chronic pain with mediators of central and peripheral neuroinflammation and immunometabolism on a molecular level. However, to address the needs for predictive factors and biomarkers, large-scale databank driven clinical trials are needed to determine the clinical value of molecular profiling.

Functional criticality in the human brain: Physiological, behavioral and neurodevelopmental correlates

Understanding the critical features of the human brain at multiple time scales is vital for both normal development and disease research. A recently proposed method, the vertex-wise Index of Functional Criticality (vIFC) based on fMRI, has been testified as a sensitive neuroimaging marker to characterize critical transitions of human brain dynamics during Alzheimer's disease progression. However, it remains unclear whether vIFC in healthy brains is associated with neuropsychological and neurophysiological measurements. Using the Nathan Kline Institute/Rockland lifespan cross-sectional datasets and openfMRI single participant longitudinal datasets, we found consistent spatial patterns of vIFC across the entire cortical mantle: the inferior parietal and the precuneus exhibited high vIFC. On a time scale of years, we observed that vIFC increased with age in the left ventral posterior cingulate gyrus. On a time scale of days and weeks, vIFC demonstrated the capacity to identify a link between anxiety and pulse. These results showed that vIFC can serve as a useful neuroimaging marker for detecting physiological, behavioral, and neurodevelopmental transitions. Based on the criticality theory in nonlinear dynamics, the current vIFC study sheds new light on human brain studies from a nonlinear perspective and opens potential new avenues for normal and abnormal human brain studies.

Evolution of extrema features reveals optimal stimuli for biological state transitions

The ability to define the unique features of an input stimulus needed to control switch-like behavior in biological systems is an important problem in computational biology and medicine. We show in this study how highly complex and intractable optimization problems can be simplified by restricting the search to the signal's extrema as key feature points, and evolving the extrema features towards optimal solutions that closely match solutions derived from gradient-based methods. Our results suggest a model-independent approach for solving a class of optimization problems related to controlling switch-like state transitions.

Impaired Functional Criticality of Human Brain during Alzheimer's Disease Progression

The progression of Alzheimer’s Disease (AD) has been proposed to comprise three stages, subjective cognitive decline (SCD), mild cognitive impairment (MCI), and AD. Was brain dynamics across the three stages smooth? Was there a critical transition? How could we characterize and study functional criticality of human brain? Based on dynamical characteristics of critical transition from nonlinear dynamics, we proposed a vertex-wise Index of Functional Criticality (vIFC) of fMRI time series in this study. Using 42 SCD, 67 amnestic MCI (aMCI), 34 AD patients as well as their age-, sex-, years of education-matched 54 NC, our new method vIFC successfully detected significant patient-normal differences for SCD and aMCI, as well as significant negative correlates of vIFC in the right middle temporal gyrus with total scores of Montreal Cognitive Assessment (MoCA) in SCD. In comparison, standard deviation of fMRI time series only detected significant differences between AD patients and normal controls. As an index of functional criticality of human brain derived from nonlinear dynamics, vIFC could serve as a sensitive neuroimaging marker for future studies; considering much more vIFC impairments in aMCI compared to SCD and AD, our study indicated aMCI as a critical stage across AD progression.

Several Indicators of Critical Transitions for Complex Diseases Based on Stochastic Analysis

Many complex diseases (chronic disease onset, development and differentiation, self-assembly, etc.) are reminiscent of phase transitions in a dynamical system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. Understanding such nonlinear behaviors is critical to dissect the multiple genetic/environmental factors that together shape the genetic and physiological landscape underlying basic biological functions and to identify the key driving molecules. Based on stochastic differential equation (SDE) model, we theoretically derive three statistical indicators, that is, coefficient of variation (CV), transformed Pearson's correlation coefficient (TPC), and transformed probability distribution (TPD), to identify critical transitions and detect the early-warning signals of the phase transition in complex diseases. To verify the effectiveness of these early-warning indexes, we use high-throughput data for three complex diseases, including influenza caused by either H3N2 or H1N1 and acute lung injury, to extract the dynamical network biomarkers (DNBs) responsible for catastrophic transition into the disease state from predisease state. The numerical results indicate that the derived indicators provide a data-based quantitative analysis for early-warning signals for critical transitions in complex diseases or other dynamical systems.

ATP1A2 Mutations in Migraine: Seeing through the Facets of an Ion Pump onto the Neurobiology of Disease

Mutations in four genes have been identified in familial hemiplegic migraine (FHM), from which CACNA1A (FHM type 1) and SCN1A (FHM type 3) code for neuronal voltage-gated calcium or sodium channels, respectively, while ATP1A2 (FHM type 2) encodes the α2 isoform of the Na(+),K(+)-ATPase's catalytic subunit, thus classifying FHM primarily as an ion channel/ion transporter pathology. FHM type 4 is attributed to mutations in the PRRT2 gene, which encodes a proline-rich transmembrane protein of as yet unknown function. The Na(+),K(+)-ATPase maintains the physiological gradients for Na(+) and K(+) ions and is, therefore, critical for the activity of ion channels and transporters involved neuronal excitability, neurotransmitter uptake or Ca(2+) signaling. Strikingly diverse functional abnormalities have been identified for disease-linked ATP1A2 mutations which frequently lead to changes in the enzyme's voltage-dependent properties, kinetics, or apparent cation affinities, but some mutations are truly deleterious for enzyme function and thus cause full haploinsufficiency. Here, we summarize structural and functional data about the Na(+),K(+)-ATPase available to date and an overview is provided about the particular properties of the α2 isoform that explain its physiological relevance in electrically excitable tissues. In addition, current concepts about the neurobiology of migraine, the correlations between primary brain dysfunction and mechanisms of headache pain generation are described, together with insights gained recently from modeling approaches in computational neuroscience. Then, a survey is given about ATP1A2 mutations implicated in migraine cases as documented in the literature with focus on mutations that were described to completely destroy enzyme function, or lead to misfolded or mistargeted protein in particular model cell lines. We also discuss whether or not there are correlations between these most severe mutational effects and clinical phenotypes. Finally, perspectives for future research on the implications of Na(+),K(+)-ATPase mutations in human pathologies are presented.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.

Understanding migraine using dynamic network biomarkers

Background

Mathematical modeling approaches are becoming ever more established in clinical neuroscience. They provide insight that is key to understanding complex interactions of network phenomena, in general, and interactions within the migraine-generator network, in particular.

Purpose

In this study, two recent modeling studies on migraine are set in the context of premonitory symptoms that are easy to confuse for trigger factors. This causality confusion is explained, if migraine attacks are initiated by a transition caused by a tipping point.

Conclusion

We need to characterize the involved neuronal and autonomic subnetworks and their connections during all parts of the migraine cycle if we are ever to understand migraine. We predict that mathematical models have the potential to dismantle large and correlated fluctuations in such subnetworks as a dynamic network biomarker of migraine.

Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of ionic excitability that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na⁺/K⁺ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na⁺/K⁺ pumps, and other proteins that regulate ion homeostasis.