Mathematical Modelling with Multidisciplinary Applications (M3A)http://hdl.handle.net/20.500.11824/132019-11-14T08:45:06Z2019-11-14T08:45:06ZMeta-modeling on detailed geography for accurate prediction of invasive alien species dispersalPepper N.Gerardo-Giorda L.Montomoli F.http://hdl.handle.net/20.500.11824/10402019-11-08T02:00:11Z2019-11-07T00:00:00ZMeta-modeling on detailed geography for accurate prediction of invasive alien species dispersal
Pepper N.; Gerardo-Giorda L.; Montomoli F.
Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.
2019-11-07T00:00:00ZClinical correlates of mathematical modeling of cortical spreading depression: Single‐cases studyKroos J.M.de Tommaso M.Stramaglia S.Vecchio E.Burdi N.Gerardo Giorda L.http://hdl.handle.net/20.500.11824/10272019-10-12T01:00:11Z2019-07-28T00:00:00ZClinical correlates of mathematical modeling of cortical spreading depression: Single‐cases study
Kroos J.M.; de Tommaso M.; Stramaglia S.; Vecchio E.; Burdi N.; Gerardo Giorda L.
Introduction: Considerable connections between migraine with aura and cortical spreading depression (CSD), a depolarization wave originating in the visual cortex and traveling toward the frontal lobe, lead to the hypothesis that CSD is underlying migraine aura. The highly individual and complex characteristics of the brain cor‐ tex suggest that the geometry might impact the propagation of cortical spreading depression.
Methods: In a single‐case study, we simulated the CSD propagation for five migraine with aura patients, matching their symptoms during a migraine attack to the CSD wavefront propagation. This CSD wavefront was simulated on a patient‐specific tri‐ angulated cortical mesh obtained from individual MRI imaging and personalized dif‐ fusivity tensors derived locally from diffusion tensor imaging data.
Results: The CSD wave propagation was simulated on both hemispheres, despite in all but one patient the symptoms were attributable to one hemisphere. The CSD wave diffused with a large wavefront toward somatosensory and prefrontal regions, devoted to pain processing.
Discussion: This case‐control study suggests that the cortical geometry may con‐ tribute to the modality of CSD evolution and partly to clinical expression of aura symptoms. The simulated CSD is a large and diffuse phenomenon, possibly capa‐ ble to activate trigeminal nociceptors and to involve cortical areas devoted to pain processing.
2019-07-28T00:00:00ZA roadmap to integrate astrocytes into Systems NeuroscienceKastanenka Ksenia V.Poskanzer Kira E.Galea ElenaMoreno-Bote R.De Pittà M.Perea G.Eraso-Pichot A.Masgrau R.http://hdl.handle.net/20.500.11824/10182019-10-09T01:00:13Z2019-05-06T00:00:00ZA roadmap to integrate astrocytes into Systems Neuroscience
Kastanenka Ksenia V.; Poskanzer Kira E.; Galea Elena; Moreno-Bote R.; De Pittà M.; Perea G.; Eraso-Pichot A.; Masgrau R.
Systems Neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca$^{2+}$ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in time scales of sub-seconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, are, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration, such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca$^{2+}$ and brain coding may represent a leap forward towards novel approaches in the study of astrocytes in health and disease.
2019-05-06T00:00:00ZMetastable resting state brain dynamicsbeim Graben P.Jimenez-Marin A.Diez I.Cortes J. M.Desroches M.Rodrigues S.http://hdl.handle.net/20.500.11824/10162019-09-30T01:00:10Z2019-09-06T00:00:00ZMetastable resting state brain dynamics
beim Graben P.; Jimenez-Marin A.; Diez I.; Cortes J. M.; Desroches M.; Rodrigues S.
Metastability refers to the fact that the state of a dynamical system spends a large amount of time in a restricted region of its available phase space before a transition takes place, bringing the system into another state from where it might recur into the previous one. Beim Graben and Hutt suggested to use the recurrence plot (RP) technique introduced by Eckmann et al. for the segmentation of system’s trajectories into metastable states using recurrence grammars. Here, we apply this recurrence structure analysis (RSA) for the first time to resting-state brain dynamics obtained from functional magnetic resonance imaging (fMRI). Brain regions are defined according to the brain hierarchical atlas (BHA) developed by Diez et al., and as a consequence, regions present high-connectivity in both structure (obtained from diffusion tensor imaging) and function (from the blood-level dependent-oxygenation —BOLD— signal). Remarkably, regions observed by Diez et al. were completely time-invariant. Here, in order to compare this static picture with the metastable systems dynamics obtained from the RSA segmentation, we determine the number of metastable states as a measure of complexity for all subjects and for region numbers varying from 3 to 100. We find RSA convergence towards an optimal segmentation of 40 metastable states for normalized BOLD signals, averaged over BHA modules. Next, we build a bistable dynamics at population level by pooling 30 subjects after Hausdorff clustering. In link with this finding, we reflect on the different modeling frameworks that can allow for such scenarios: heteroclinic dynamics, dynamics with riddled basins of attraction, multiple-timescale dynamics. Finally, we characterize the metastable states both functionally and structurally, using templates for resting state networks (RSNs) and the automated anatomical labeling (AAL) atlas, respectively.
2019-09-06T00:00:00Z