A computational multiscale model of cortical spreading depression propagation

Cortical Spreading Depression (CSD) is a disruption of the brain hemostasis that, originating in the visual cortex and traveling towards the frontal lobe, temporarily impairs the normal functioning of neurons. Although, as of today, little is known about the mechanisms that can trigger or stop such phenomenon, CSD is commonly accepted as a correlate of migraine visual aura. In this paper, we introduce a multiscale PDE-ODE model that couples the propagation of the depolarization wave associated to CSD with a detailed electrophysiological model for the neuronal activity to capture both macroscopic and microscopic dynamics

Temporal excitation patterns on the cerebral cortex as a result of migraine modeling

The complex, highly individual, geometry of the cerebral cortex in humans presents a major challenge in studying the spreading of spontaneous neuronal activity. Recent computational advances [1] allow to simulate the propagation of depolarization waves on the macroscale and for individual geometries, reconstructed from accurate medical imaging as MRI, with high levels of detail. In this paper we take advantage of such technique to study the temporal excitation patterns that follow the passage of a depolarization wave on the cerebral cortex.This work was supported by the Bizkaia Talent and European Commission through COFUND under the grant BRAhMS – Brain Aura Mathematical Simulation– (AYD-000- 285), and also by the Basque Government through the BERC 2014-2017 program, and by the Spanish Ministry of Economics and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323. JMC acknowledges financial support from Ikerbasque: The Basque Foundation for Science and Euskampus at UPV/EHU

Geometry shapes propagation: Assessing the presence and absence of cortical symmetries through a computational model of cortical spreading depression

Cortical spreading depression (CSD), a depolarization wave which originates in the visual cortex and travels toward the frontal lobe, has been suggested to be one neural correlate of aura migraine. To the date, little is known about the mechanisms which can trigger or stop aura migraine. Here, to shed some light on this problem and, under the hypothesis that CSD might mediate aura migraine, we aim to study different aspects favoring or disfavoring the propagation of CSD. In particular, by using a computational neuronal model distributed throughout a realistic cortical mesh, we study the role that the geometry has in shaping CSD. Our results are two-fold: first, we found significant differences in the propagation traveling patterns of CSD, both intra and inter-hemispherically, revealing important asymmetries in the propagation profile. Second, we developed methods able to identify brain regions featuring a peculiar behavior during CSD propagation. Our study reveals dynamical aspects of CSD, which, if applied to subject-specific cortical geometry, might shed some light on how to differentiate between healthy subjects and those suffering migraine

Patient-specific computational modeling of Cortical Spreading Depression via Diffusion Tensor Imaging

Cortical Spreading Depression (CSD), a depolarization wave originat- ing in the visual cortex and traveling towards the frontal lobe, is com- monly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in sup- porting or contrasting the propagation of CSD. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisa- tion in the grey matter. In this paper we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from Diffusion Tensor Imaging data.This work was supported by the Bizkaia Talent and European Commission through COFUND under the grant BRAhMS - Brain Aura Mathematical Sim- ulation (AYD-000-285), by the Basque Government through the BERC 2014- 2017 program, and by the Spanish Ministry of Economics and Competitiveness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013- 0323 and the Spanish "Plan Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad" under Grant BELEMET - Brain ELEctro- METabolic modeling and numerical approximation (MTM2015-69992-R). JMC acknowledges financial support from Ikerbasque: The Basque Foundation for Science and Euskampus at UPV/EHU

Clinical correlates of mathematical modeling of cortical spreading depression: Single‐cases study

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

Isolation of the Two Monoferric Human Transferrins by Preparative Isoelectric Focussing

Peer Reviewe

Mucopolysaccharidosis type VI phenotypes-genotypes and antibody response to galsulfase

Background: Mucopolysaccharidosis type VI (Maroteaux-Lamy syndrome; MPS VI) is an autosomal recessive lysosomal storage disorder in which deficiency of N-acetylgalactosamine 4-sulfatase (arylsulfatase B; ARSB) leads to the storage of glycosaminoglycans (GAGs) in connective tissue. The genotype-phenotype correlation has been addressed in several publications but the picture is not complete. Since 2007, enzyme-replacement therapy (ERT) has been available for patients with MPS VI in the Netherlands. The purpose of our study was to learn more about the genotype-phenotype correlations in MPS VI and the antibody response to ERT with galsulfase (recombinant human arylsulfatase B). Methods. We identified ARSB mutations in 12 patients and used site-directed mutagenesis to study their effect. Antibody levels to galsulfase were measured using ELISA and a semi-quantitative immunoprecipitation method. We assessed the in vitro inhibitory effect of antibodies on galsulfase uptake and their effect on clinical outcome. Results: Five patients had a rapidly progressive phenotype and seven a slowly progressive phenotype. In total 9 pathogenic mutations were identified including 4 novel mutations (N301K, V332G, A237D, and c.1142 + 2 T > C) together composing 8 pathogenic genotypes. Most mutations appeared not to affect the synthesis of ARSB (66 kD precursor), but to hamper its maturation (43 kD ARSB). Disease severity was correlated with urinary GAG excretion. All patients developed antibodies to galsulfase within 26 weeks of treatment. It was demonstrated that these antibodies can inhibit the uptake of galsulfase in vitro. Conclusions: The clinical phenotypes and the observed defects in the biosynthesis of ARSB show that some of the mutations that we identified are clearly more severe than others. Patients receiving galsulfase as enzyme-replacement therapy can develop antibodies towards the therapeutic protein. Though most titers are modest, they can exceed a level at which they potentially affect the clinical outcome of enzyme-replacement therapy

Should we teach linear algebra through geometry?

AbstractCan geometry help students learn linear algebra? I study this question and demonstrate that there is no obvious clear answer: geometry can be an obstacle to learning linear algebra; or it can be helpful. Geometry is helpful only under certain conditions and with a specific use of drawings. These special requirements for using geometry are apparently not much recognized in our teaching of linear algebra courses, at least in France, where my educational studies have taken place