(i) Dynamical network biomarkers can help identify the key subnetworks that drive migraine transitions from the prodrome phase to the pain phase. Large fluctuations in cerebral blood flow control and a highly variable pattern of free energy starvation within the migraine generator network may contribute to these transitions.
(ii) Spreading depression triggers headache by activating neuronal PANX1 channels.
(iii) M. Dahlem proposes that the migraine generator network and spreading depression dynamics are promising targets for neuromodulation in episodic migraine.
The document discusses migraine and mathematical models. It provides an overview of migraine research topics including migraine pain pathways and modulation, cortical architecture and visual hallucinations, and macroscopic reaction-diffusion patterns in migraine. Mathematical models of migraine discussed include macroscopic models using reaction-diffusion equations to model traveling wave solutions, as well as ion-based cellular models. Open questions remain about the common etiology of migraine with and without aura and the relationship between spreading depression waves and migraine aura symptoms.
Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electrical and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. First, we will present models of slow dynamics emerging on large cortical scales controlled by both subcortical networks and neurovascular coupling. The focus is on modeling migraine, though this approach is nested within the wider interest in modeling slow and large-scale dynamics in the brain. The aim is not only to better understand pain conditions and fluctuations in the resting state that causes these conditions but also to identify new opportunities to intervene with medical devices and implantable neuroprostheses. To this end, we then present the relevant state of the art of neuromodulation in migraine and approaches in fusion of both developments towards a translational computational neuroscience.
The document presents a unifying framework for modeling ion dynamics in the brain that can explain phenomena seen in epilepsy, migraine, and stroke. It introduces a second generation of Hodgkin-Huxley type models that account for ion concentrations and pumping/buffering dynamics in addition to membrane voltage dynamics. These models exhibit bistability between polarized and depolarized states, depending on parameters. The framework aims to provide a common mechanistic explanation for different neurological disorders based on shifts between stable states induced by genetic or external factors.
Computational Motor Control: Introduction (JAIST summer course)hirokazutanaka
This is a course introduction to JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). https://www.youtube.com/user/ht2022columbia
Reentrant and retracting waves of cortical spreading depression in migraineMPI Dresden / HU Berlin
1. The document discusses spreading depression, which are waves of depolarization that spread across brain tissue.
2. It describes how spreading depression waves can be reentrant and retracting in the cortex, forming complex spatiotemporal patterns.
3. The document suggests that understanding spreading depression waves could help explain migraine as a dynamical disease and help develop new therapies.
Computational Motor Control: Optimal Control for Deterministic Systems (JAIST...hirokazutanaka
This is lecure 2 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=lNH1q4y1m-U
The document discusses migraine and mathematical models. It provides an overview of migraine research topics including migraine pain pathways and modulation, cortical architecture and visual hallucinations, and macroscopic reaction-diffusion patterns in migraine. Mathematical models of migraine discussed include macroscopic models using reaction-diffusion equations to model traveling wave solutions, as well as ion-based cellular models. Open questions remain about the common etiology of migraine with and without aura and the relationship between spreading depression waves and migraine aura symptoms.
Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electrical and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. First, we will present models of slow dynamics emerging on large cortical scales controlled by both subcortical networks and neurovascular coupling. The focus is on modeling migraine, though this approach is nested within the wider interest in modeling slow and large-scale dynamics in the brain. The aim is not only to better understand pain conditions and fluctuations in the resting state that causes these conditions but also to identify new opportunities to intervene with medical devices and implantable neuroprostheses. To this end, we then present the relevant state of the art of neuromodulation in migraine and approaches in fusion of both developments towards a translational computational neuroscience.
The document presents a unifying framework for modeling ion dynamics in the brain that can explain phenomena seen in epilepsy, migraine, and stroke. It introduces a second generation of Hodgkin-Huxley type models that account for ion concentrations and pumping/buffering dynamics in addition to membrane voltage dynamics. These models exhibit bistability between polarized and depolarized states, depending on parameters. The framework aims to provide a common mechanistic explanation for different neurological disorders based on shifts between stable states induced by genetic or external factors.
Computational Motor Control: Introduction (JAIST summer course)hirokazutanaka
This is a course introduction to JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). https://www.youtube.com/user/ht2022columbia
Reentrant and retracting waves of cortical spreading depression in migraineMPI Dresden / HU Berlin
1. The document discusses spreading depression, which are waves of depolarization that spread across brain tissue.
2. It describes how spreading depression waves can be reentrant and retracting in the cortex, forming complex spatiotemporal patterns.
3. The document suggests that understanding spreading depression waves could help explain migraine as a dynamical disease and help develop new therapies.
Computational Motor Control: Optimal Control for Deterministic Systems (JAIST...hirokazutanaka
This is lecure 2 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=lNH1q4y1m-U
Computational Motor Control: Kinematics & Dynamics (JAIST summer course)hirokazutanaka
Computational Motor Control: Kinematics & Dynamics (JAIST summer course)
This is lecture 1 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=8nk4DlpAaS8
Computational Motor Control: Optimal Estimation in Noisy World (JAIST summer ...hirokazutanaka
This is lecure 4 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=2-VRBIg5m0w
This document discusses mathematical models of migraine. It begins by explaining migraine as a dynamical disease and how models can help fill gaps in understanding across scales from molecules to the entire brain. It then provides two examples of migraine models: (1) a model of spreading depression that uses reaction-diffusion equations to model ion concentration changes and (2) a model analyzing the neuron as an analogy to a heat engine with ion fluxes and reservoirs. The document outlines how these and other models can provide insights towards therapeutic intervention for migraine.
Computational Motor Control: Reinforcement Learning (JAIST summer course) hirokazutanaka
This is lecure 6 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=GHMcx5F0_j8
Recurrence Quantification Analysis :Tutorial & application to eye-movement dataDeb Aks
This document provides an overview of recurrence quantification analysis (RQA) and its application to analyzing eye movement data. RQA uses time series analysis techniques like phase space reconstruction to detect recurring patterns in complex systems. It was applied to study whether the recurring dynamics of eye movements can serve as a memory to sustain object tracking over time and during interruptions. The document reviews key concepts in RQA like delay coordinates, embedding dimension estimation, recurrence plots, and measures like determinism, laminarity, and trapping time. It includes examples of RQA applied to simulated sine waves and analyses the steps involved in conducting RQA on human eye tracking data.
Computational Motor Control: Optimal Control for Stochastic Systems (JAIST su...hirokazutanaka
This is lecure 5 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=XS7MDRMPQfU
JAISTサマースクール2016「脳を知るための理論」講義01 Single neuron modelshirokazutanaka
This document provides an overview of topics to be covered in a lecture on single neuron models. It will discuss:
1) The basic anatomy and physiology of neurons including their morphology and membrane properties.
2) Phenomenological models of subthreshold dynamics like the integrate-and-fire, quadratic-and-fire, and resonate-and-fire models.
3) Biophysical models of spiking mechanisms including the Hodgkin-Huxley model and its use of ion channels and master equations.
4) Analysis techniques like phase plots and bifurcation analysis applied to models like FitzHugh-Nagumo and Hindmarsh-Rose.
5) Modern single neuron models such
Computational Motor Control: State Space Models for Motor Adaptation (JAIST s...hirokazutanaka
This is lecure 3 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=dtpgJLRt90M
The document summarizes key concepts about the Hopfield model, an attractor neural network model inspired by physics. It discusses how memory is stored in the symmetric connectivity matrix through Hebbian learning of stored patterns. During recall, the network dynamics relax toward one of the stored memory patterns as an attractor state. This can be modeled deterministically or stochastically. The number of memories an N-neuron network can reliably store is approximately 0.15N.
JAISTサマースクール2016「脳を知るための理論」講義04 Neural Networks and Neuroscience hirokazutanaka
This document summarizes key concepts from a lecture on neural networks and neuroscience:
- Single-layer neural networks like perceptrons can only learn linearly separable patterns, while multi-layer networks can approximate any function. Backpropagation enables training multi-layer networks.
- Recurrent neural networks incorporate memory through recurrent connections between units. Backpropagation through time extends backpropagation to train recurrent networks.
- The cerebellum functions similarly to a perceptron for motor learning and control. Its feedforward circuitry from mossy fibers to Purkinje cells maps to the layers of a perceptron.
This lecture discusses synaptic learning rules in neural networks. It introduces the basic anatomy and physiology of synapses and different coding schemes neurons use, such as rate coding and spike timing coding. It then covers several synaptic plasticity rules, including Hebbian learning, spike-timing dependent plasticity (STDP), and the Bienenstock-Cooper-Munro (BCM) rule. It also discusses modeling synapses using the conductance-based model and implementations of STDP learning through online learning rules and weight dependence mechanisms.
Mike Bue is the qualified person who approved the technical information in the presentation. The presentation contains forward-looking statements regarding TVI's interests in various projects which are subject to risks and uncertainties. TVI is focused on acquiring resource projects in Asia Pacific that can be rapidly developed and put into production, and holds a 30.66% interest in TVIRD, a Philippine company developing the Agata nickel laterite and limestone projects.
Santiago Moral Rubio, Director de Seguridad de la Innovación del Grupo BBVA, ...BBVAtech
Santiago Moral Rubio, Director de Seguridad de la Innovación del Grupo BBVA, describe en la revista GMV news las principales características de la seguridad financiera.
This document discusses the properties of visible light and color. It explains that visible light is the narrow range of wavelengths within the electromagnetic spectrum that can be seen by the human eye. Differences in wavelengths are perceived as different colors. The primary colors of light are red, green, and blue, and different combinations of these colors produce other hues. The color an object appears depends on which wavelengths of light it reflects or transmits.
This document is a Construction Environmental Management Plan (CEMP) for the Rooty Hill Regional Distribution Centre Project. It provides an overview of the project and establishes a framework to manage environmental aspects during site preparation and construction works. The objectives of the CEMP are to minimize impacts on the environment and ensure statutory environmental requirements are clearly defined and met. The CEMP will be reviewed and revised as needed to address future construction activities and stages of the project. It is intended to be used as a working document by all staff and contractors during construction.
Este documento presenta los principios fundamentales del paradigma ágil y aborda conceptos erróneos comunes sobre el mismo. Explica que ágil define una cultura que garantiza la entrega exitosa de productos mediante el respeto, la construcción colaborativa y una organización flexible. También identifica errores comunes como pensar que ágil es solo una metodología, que requiere convencer a otros o que solo se aplica a ciertos proyectos.
El documento habla sobre las energías renovables en Mendoza, Argentina. Menciona que la hidroelectricidad ha sido la principal fuente renovable utilizada en la provincia desde 1926 a través de 13 centrales hidroeléctricas. También destaca que en los años 90 se instaló el primer "Pueblo Solar" en San José, proporcionando energía solar a 400 personas, y que actualmente la energía solar se distribuye ampliamente en toda la provincia. Alienta a seguir avanzando en el uso de energías limpias.
This study used 3T magnetic resonance angiography (MRA) to measure blood vessel diameters and blood flow in the brains of 32 migraine patients at three time points: baseline outside of an attack, during infusion of nitroglycerine (NTG) or placebo, and during a subsequent migraine attack or 6 hours after infusion. NTG successfully provoked migraine in 20 of 27 patients who received it but none of the 5 who received placebo. During attacks, blood vessel diameters and blood flows did not differ from baseline measurements, indicating that migraine attacks are not associated with vasodilation of cerebral or meningeal blood vessels. This suggests that vasoconstriction may not be required for acute migraine treatment.
Abnormal changes in cortical activity in women with migraine bet.docxdaniahendric
The document describes a study that used magnetoencephalography (MEG) to investigate differences in cortical excitability between migraine patients and healthy controls. MEG recordings were obtained from 35 migraine patients experiencing a headache and 35 healthy controls during an auditory-motor task. Analysis of low and high frequency neuromagnetic signals at sensor and source levels found that high frequency signals showed greater heterogeneous cortical activation in migraine patients compared to controls. The degree of heterogeneous cortical activation correlated with headache frequency. This suggests cortical excitability is altered in a spatially heterogeneous and frequency dependent manner in migraine patients.
Brief overview of brain stimulation techniquesSujit Kumar Kar
This document discusses various neurostimulation techniques used to treat psychiatric and neurological conditions. It begins by outlining the history and milestones of different brain stimulation methods from the 18th century to present day. These include the first reported use of camphor-induced seizures in 1785 to treat conditions, and the development of electroconvulsive therapy (ECT) in the 1930s-1950s.
The document then provides an overview of current neurostimulation techniques like ECT, transcranial magnetic stimulation (TMS), deep brain stimulation (DBS), vagus nerve stimulation (VNS), and transcranial direct current stimulation (tDCS). It notes their effectiveness for treating various disorders such as depression, OCD, anxiety
Computational Motor Control: Kinematics & Dynamics (JAIST summer course)hirokazutanaka
Computational Motor Control: Kinematics & Dynamics (JAIST summer course)
This is lecture 1 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=8nk4DlpAaS8
Computational Motor Control: Optimal Estimation in Noisy World (JAIST summer ...hirokazutanaka
This is lecure 4 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=2-VRBIg5m0w
This document discusses mathematical models of migraine. It begins by explaining migraine as a dynamical disease and how models can help fill gaps in understanding across scales from molecules to the entire brain. It then provides two examples of migraine models: (1) a model of spreading depression that uses reaction-diffusion equations to model ion concentration changes and (2) a model analyzing the neuron as an analogy to a heat engine with ion fluxes and reservoirs. The document outlines how these and other models can provide insights towards therapeutic intervention for migraine.
Computational Motor Control: Reinforcement Learning (JAIST summer course) hirokazutanaka
This is lecure 6 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=GHMcx5F0_j8
Recurrence Quantification Analysis :Tutorial & application to eye-movement dataDeb Aks
This document provides an overview of recurrence quantification analysis (RQA) and its application to analyzing eye movement data. RQA uses time series analysis techniques like phase space reconstruction to detect recurring patterns in complex systems. It was applied to study whether the recurring dynamics of eye movements can serve as a memory to sustain object tracking over time and during interruptions. The document reviews key concepts in RQA like delay coordinates, embedding dimension estimation, recurrence plots, and measures like determinism, laminarity, and trapping time. It includes examples of RQA applied to simulated sine waves and analyses the steps involved in conducting RQA on human eye tracking data.
Computational Motor Control: Optimal Control for Stochastic Systems (JAIST su...hirokazutanaka
This is lecure 5 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=XS7MDRMPQfU
JAISTサマースクール2016「脳を知るための理論」講義01 Single neuron modelshirokazutanaka
This document provides an overview of topics to be covered in a lecture on single neuron models. It will discuss:
1) The basic anatomy and physiology of neurons including their morphology and membrane properties.
2) Phenomenological models of subthreshold dynamics like the integrate-and-fire, quadratic-and-fire, and resonate-and-fire models.
3) Biophysical models of spiking mechanisms including the Hodgkin-Huxley model and its use of ion channels and master equations.
4) Analysis techniques like phase plots and bifurcation analysis applied to models like FitzHugh-Nagumo and Hindmarsh-Rose.
5) Modern single neuron models such
Computational Motor Control: State Space Models for Motor Adaptation (JAIST s...hirokazutanaka
This is lecure 3 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=dtpgJLRt90M
The document summarizes key concepts about the Hopfield model, an attractor neural network model inspired by physics. It discusses how memory is stored in the symmetric connectivity matrix through Hebbian learning of stored patterns. During recall, the network dynamics relax toward one of the stored memory patterns as an attractor state. This can be modeled deterministically or stochastically. The number of memories an N-neuron network can reliably store is approximately 0.15N.
JAISTサマースクール2016「脳を知るための理論」講義04 Neural Networks and Neuroscience hirokazutanaka
This document summarizes key concepts from a lecture on neural networks and neuroscience:
- Single-layer neural networks like perceptrons can only learn linearly separable patterns, while multi-layer networks can approximate any function. Backpropagation enables training multi-layer networks.
- Recurrent neural networks incorporate memory through recurrent connections between units. Backpropagation through time extends backpropagation to train recurrent networks.
- The cerebellum functions similarly to a perceptron for motor learning and control. Its feedforward circuitry from mossy fibers to Purkinje cells maps to the layers of a perceptron.
This lecture discusses synaptic learning rules in neural networks. It introduces the basic anatomy and physiology of synapses and different coding schemes neurons use, such as rate coding and spike timing coding. It then covers several synaptic plasticity rules, including Hebbian learning, spike-timing dependent plasticity (STDP), and the Bienenstock-Cooper-Munro (BCM) rule. It also discusses modeling synapses using the conductance-based model and implementations of STDP learning through online learning rules and weight dependence mechanisms.
Mike Bue is the qualified person who approved the technical information in the presentation. The presentation contains forward-looking statements regarding TVI's interests in various projects which are subject to risks and uncertainties. TVI is focused on acquiring resource projects in Asia Pacific that can be rapidly developed and put into production, and holds a 30.66% interest in TVIRD, a Philippine company developing the Agata nickel laterite and limestone projects.
Santiago Moral Rubio, Director de Seguridad de la Innovación del Grupo BBVA, ...BBVAtech
Santiago Moral Rubio, Director de Seguridad de la Innovación del Grupo BBVA, describe en la revista GMV news las principales características de la seguridad financiera.
This document discusses the properties of visible light and color. It explains that visible light is the narrow range of wavelengths within the electromagnetic spectrum that can be seen by the human eye. Differences in wavelengths are perceived as different colors. The primary colors of light are red, green, and blue, and different combinations of these colors produce other hues. The color an object appears depends on which wavelengths of light it reflects or transmits.
This document is a Construction Environmental Management Plan (CEMP) for the Rooty Hill Regional Distribution Centre Project. It provides an overview of the project and establishes a framework to manage environmental aspects during site preparation and construction works. The objectives of the CEMP are to minimize impacts on the environment and ensure statutory environmental requirements are clearly defined and met. The CEMP will be reviewed and revised as needed to address future construction activities and stages of the project. It is intended to be used as a working document by all staff and contractors during construction.
Este documento presenta los principios fundamentales del paradigma ágil y aborda conceptos erróneos comunes sobre el mismo. Explica que ágil define una cultura que garantiza la entrega exitosa de productos mediante el respeto, la construcción colaborativa y una organización flexible. También identifica errores comunes como pensar que ágil es solo una metodología, que requiere convencer a otros o que solo se aplica a ciertos proyectos.
El documento habla sobre las energías renovables en Mendoza, Argentina. Menciona que la hidroelectricidad ha sido la principal fuente renovable utilizada en la provincia desde 1926 a través de 13 centrales hidroeléctricas. También destaca que en los años 90 se instaló el primer "Pueblo Solar" en San José, proporcionando energía solar a 400 personas, y que actualmente la energía solar se distribuye ampliamente en toda la provincia. Alienta a seguir avanzando en el uso de energías limpias.
This study used 3T magnetic resonance angiography (MRA) to measure blood vessel diameters and blood flow in the brains of 32 migraine patients at three time points: baseline outside of an attack, during infusion of nitroglycerine (NTG) or placebo, and during a subsequent migraine attack or 6 hours after infusion. NTG successfully provoked migraine in 20 of 27 patients who received it but none of the 5 who received placebo. During attacks, blood vessel diameters and blood flows did not differ from baseline measurements, indicating that migraine attacks are not associated with vasodilation of cerebral or meningeal blood vessels. This suggests that vasoconstriction may not be required for acute migraine treatment.
Abnormal changes in cortical activity in women with migraine bet.docxdaniahendric
The document describes a study that used magnetoencephalography (MEG) to investigate differences in cortical excitability between migraine patients and healthy controls. MEG recordings were obtained from 35 migraine patients experiencing a headache and 35 healthy controls during an auditory-motor task. Analysis of low and high frequency neuromagnetic signals at sensor and source levels found that high frequency signals showed greater heterogeneous cortical activation in migraine patients compared to controls. The degree of heterogeneous cortical activation correlated with headache frequency. This suggests cortical excitability is altered in a spatially heterogeneous and frequency dependent manner in migraine patients.
Brief overview of brain stimulation techniquesSujit Kumar Kar
This document discusses various neurostimulation techniques used to treat psychiatric and neurological conditions. It begins by outlining the history and milestones of different brain stimulation methods from the 18th century to present day. These include the first reported use of camphor-induced seizures in 1785 to treat conditions, and the development of electroconvulsive therapy (ECT) in the 1930s-1950s.
The document then provides an overview of current neurostimulation techniques like ECT, transcranial magnetic stimulation (TMS), deep brain stimulation (DBS), vagus nerve stimulation (VNS), and transcranial direct current stimulation (tDCS). It notes their effectiveness for treating various disorders such as depression, OCD, anxiety
Significance of Brain imaging in Psychiatry. Most of the major Psychiatric disorders are associated with statistically significant differences on various Neuroimaging measures, when comparing groups of patients and controls.
Micro-Neuro-Sensor Recording of STN Neurons of the Human BrainMangaiK4
Abstract-What cause to the neurons of the human brain cells when they are damaged. They become inactive. So damage to subthalamiuc ucleus (STN) neurons of the human brain causing larger involuntary movements and thereby attacking the Parkinson’s disease (PD). Deep brain stimulation (DBS) of bilateral sub thalamic nuclei (STN) is an efficient method of rehabilitation technique in subjects with advanced idiopathic Parkinson’s (or Parkinson) disease. Accurate targeting of STN neurons and placement of microelectrodes/ (neurosensors) are paramount importance for optimal results after STN-DBS method.In this paper, microminiaturized electrode recordings (MER) of STN neurons were detected in a mean of 3.5 ±1.1 channels on right hemisphere and 3.6 ±1.04 on left hemisphere.Final channel selected were most commonly central seen in 42.3% followed by anterior in 33.7%. When a high current is delivered to STN or GPi neurons of basal ganglia (a component of human brain), causing their inhibition and improved indication of symptoms. It is now known that there is a significant change in the firing pattern and a reorganization of the entire basal ganglia circuit with DBS. The MER of STN neurons has identified a specific high frequency irregular larger amplitude firing patterns seen only in disease states and hence used to detect the neurons of ST nucleus during functional surgery. Micro electrode recording is so useful to confirm the right path but has to be taken in consideration with effects on macro stimulation.
This document summarizes a presentation given by David López Sánchez on spinal osteopathic manipulative therapy. It provides an overview of osteopathic philosophy which views the body as a single unified system. It describes assessment techniques for somatic dysfunction including asymmetry and tissue changes. Mechanisms of spinal manipulation are discussed such as restoring range of motion and reducing nociception. The document concludes that osteopathy aims to optimize health and stimulate self-regulation rather than simply treat diseases.
Transcranial direct current stimulation Andri Andri
Transracial direct current stimulation (tDCS) is a non-invasive form of brain stimulation that delivers low currents of electricity to modulate neuronal activity. It has been studied as a treatment for conditions such as depression, stroke rehabilitation and cognitive impairment. While generally safe with minor side effects like skin irritation and fatigue, more research is still needed on its efficacy and long term effects before it can be recommended in clinical practice. tDCS holds promise as a treatment to induce neuroplasticity but requires further evaluation in controlled trials.
The document discusses traumatic brain injury (TBI), including its definition, classification, mechanisms of injury, management, and oxygenation monitoring. It defines TBI as a brain disorder caused by external mechanical trauma, causing physical, cognitive and psychosocial impairments temporarily or permanently. Management involves monitoring intracranial pressure (ICP) and cerebral perfusion pressure (CPP) to prevent secondary ischemic brain injuries. Oxygenation monitoring techniques like brain tissue oxygen tension are also discussed to help determine optimal CPP thresholds for patients with TBI.
Micro-Neuro-Sensor Recording of STN Neurons of the Human Brainijcoa
What cause to the neurons of the human brain cells when they are damaged. They become inactive. So damage to subthalamiuc nucleus (STN) neurons of the human brain causing larger involuntary movements and thereby attacking the Parkinson’s disease (PD). Deep brain stimulation (DBS) of bilateral sub thalamic nuclei (STN) is an efficient method of rehabilitation technique in subjects with advanced idiopathic Parkinson’s (or Parkinson) disease. Accurate targeting of STN neurons and placement of microelectrodes/ (neurosensors) are paramount importance for optimal results after STN-DBS method.In this paper, microminiaturized electrode recordings (MER) of STN neurons were detected in a mean of 3.5 ±1.1 channels on right hemisphere and 3.6 ±1.04 on left hemisphere.Final channel selected were most commonly central seen in 42.3% followed by anterior in 33.7%. When a high current is delivered to STN or GPi neurons of basal ganglia (a component of human brain), causing their inhibition and improved indication of symptoms. It is now known that there is a significant change in the firing pattern and a reorganization of the entire basal ganglia circuit with DBS. The MER of STN neurons has identified a specific high frequency irregular larger amplitude firing patterns seen only in disease states and hence used to detect the neurons of ST nucleus during functional surgery. Microelectrode recording is so useful to confirm the right path but has to be taken in consideration with effects on macro stimulation.
MEDITATION: ITS TREMENDOUS IMPACT ON HEART RATE VARIABILITYcscpconf
The heart is connected through the nervous system directly to major organs and is able to sense
their need. The heart also responds to adrenaline in the blood flowing through it. With these
inputs the heart is able to adjust its rate to accommodate the needs of the whole body. By its
heartbeat, it is able to broadcast a common signal to every cell. One measure of heart health is
Heart Rate Variability (HRV). HRV is defined in terms of how different the lengths of time
between each heart beat is. The greater the difference in times between heart beats, the
healthier is the heart thought to be. Individuals may be able to learn to increase their own HRV
and become healthier by a daily meditation practice. This paper uses Heart Variability as the
base signal for studying the impact of meditation on it. The paper brings out the difference
between pre and post meditation conditions in terms qualitative measure of Power Spectral
Density (PSD) variations using Smoothed Pseudo Wigner Ville (SPWVD) distribution method.The simulations highlight the meditation effects overtime period in PSDs
There are two main types of MRI sequences: spin echo (SE) and gradient echo (GE). SE produces better image quality but has longer scan times, while GE has shorter scan times. Key MRI parameters are repetition time (TR) and echo time (TE). Different MRI weightings (T1, T2, PD, FLAIR) provide contrast between tissues. Advanced MRI techniques like DWI, PWI, and MRS provide additional clinical information on diffusion, perfusion, and metabolism. Functional MRI (fMRI) uses the BOLD contrast to non-invasively map functional brain activity with good spatial and temporal resolution. MRI and its variants are useful clinical tools for diagnosis, treatment planning, and studying brain
Large Vessel Stroke in Tuberculous MeningitisAhmad Ozair
Presented by an MBBS-2017 batch student in the American College of Physicians (ACP) in Lucknow on 1st September. The case was adjudged in the junior category as the 'Best Clinical Vignette'.
The case was documented by Dr Imran Rizvi of King George's Medical University and the poster was prepared by Ahmad Ozair, MBBS 2016 batch student.
The document provides an overview of neuroimaging techniques used in psychiatry such as MRI, CT, PET, SPECT, fMRI, DTI, and MRS. It discusses the basic principles, milestones in development, and applications of these techniques. Specifically, it summarizes research using these neuroimaging methods that have found abnormalities in brain structure and function in patients with obsessive-compulsive disorder (OCD), such as reduced serotonin transporter binding in fronto-striatal circuits and differences in brain activity in regions like the thalamus and orbitofrontal cortex.
Intro to Transcranial Direct Curent Stimulation (tDCS)Daniel Stevenson
This document summarizes Transcranial Direct Current Stimulation (tDCS). It discusses the history of tDCS, how it works, applications in therapeutic and enhancement contexts, physiological effects and basis, safety considerations, and the future of research. tDCS involves applying a weak electrical current to the brain via electrodes to modulate cortical excitability. It has therapeutic potential for conditions like depression, motor rehabilitation, and is being studied for cognitive enhancement. Research suggests its effects are mediated by changes in neuronal membrane potentials and synaptic plasticity.
ISMST - 2014 Presentation Final PresentationKenneth Craig
This document summarizes a case series study on the use of extracorporeal shockwave therapy (ESWT) to treat complex/neuropathic pain syndromes. It describes 12 patients who underwent 4 treatments of ESWT at weekly intervals and experienced significant reductions in pain, physical impairment, and emotional distress that were maintained at 24-week follow up based on standardized questionnaires. The proposed mechanisms of action of ESWT for neuropathic pain and rationale for its application are discussed. The study concludes that ESWT shows promise for treating neuropathic pain and warrants further research.
Presentation1, new mri techniques in the diagnosis and monitoring of multiple...Abdellah Nazeer
This document discusses new MRI techniques for diagnosing and monitoring multiple sclerosis (MS). It recommends protocols for baseline and follow-up brain and spinal cord MRIs, including mandatory and optional sequences. Advanced techniques like double inversion recovery, diffusion tensor imaging, and MR spectroscopy are highlighted for improving detection of gray matter lesions and diffuse white matter damage compared to conventional MRI. The document concludes that while conventional MRI is important for MS, advanced techniques provide higher sensitivity and specificity for both lesions and normal-appearing brain tissue, furthering understanding of MS pathophysiology.
This document discusses the MR morphology of intracranial tuberculomas based on a study of 10 patients. Key findings include:
1) Tuberculomas showed variable signals on T1 and T2 weighted MR images depending on their stage of evolution and composition.
2) Most lesions appeared hypointense on T2 weighted images due to fibrosis, scar tissue, and free radicals from macrophages.
3) MR was useful for visualizing the full extent of lesions, differentiating tuberculomas from other pathologies, and delineating internal components like necrotic centers.
4) Follow up MR in patients responding to treatment showed reduction in lesion size and surrounding edema.
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Similar a Dynamical network biomarkers in migraine (20)
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Dynamical network biomarkers in migraine
1. Dynamical network biomarkers in migraine
(a)
mi
n
ths
on
cortex
magnetic
l
HY,TH
ele
(b)
PAG
(c)
p
ay
1d
e
e
r
rom
t
td
m
cle
in e c y
o
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ctr
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Markus A. Dahlem (HU Berlin)
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
Berlin Center for Studies of Complex Chemical Systems, Jan 24, 2014
2. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion
3. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion
4. History of electrical & magnetic stimluation
Non-drug treatment for headaches (AD 47)
Scribonius Largus, court physician to the Roman emperor Claudius 47 AD used
the black torpedo fish (electric rays) to treat migraine.
5. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1788)
P. J. Koehler and C. J. Boes, A history of non-drug treatment in headache,
particularly migraine. Brain 133:2489-500. 2010
6. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1887)
P. J. Koehler and C. J. Boes, A history of non-drug treatment in headache,
particularly migraine. Brain 133:2489-500. 2010
19. Old problems remain
¨
“Uber die physiologischen Wirkungen der elektrischen B¨der liegen eine Reihe von Angaben [...] vor.
a
[...]
Im allgemeinen haben faradische B¨der einen erfrischenden Einfluß, galvanische sollen m¨de machen.
a
u
Es kommt f¨r die Wirkung entschieden auf die Dauer der B¨der an, k¨rzere werden mehr anregend, l¨ngere mehr
u
a
u
a
erschlaffend wirken.
Durchsichtig ist jedenfalls die physiologische Begr¨ndung dieser B¨der durchaus nicht, man wird sich vorstellen,
u
a
daßsie im allgemeinen die eines indifferenten Bades, mit dem ein milder Hautreiz verbunden ist, haben.
Es m¨gen dadurch Aenderungen in unseren Allgemeingef¨hlen, also Wohlbehagen, Erfrischung oder M¨digkeit
o
u
u
bedingt werden. Nach meiner Ansicht liegt aber die Hauptwirkung dieser elektrischen B¨der in erster Linie auf
a
suggestivem Gebiete, und das rechtfertigt ihre Anwendung und ihre unleugbaren Erfolge auf dem Gebiete der
nerv¨sen Allgemeinleiden, wie Hysterie, Neurasthenie etc.”
o
(Lehrbuch der klinischen Hydrotherapie, Max Matthes)
20. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion
21. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
22. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
23. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
24. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
25. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
26. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
SPG
(iii)
SSN
p
y
a
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
27. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
SPG
(iii)
SSN
p
y
a
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
28. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
29. a ur a
(i)
m
on
cle
in e c y
cortex
p
y
a
1d
HY,TH
magnetic
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
igr
a
os
ths
e
4 -72h
(avg 2 we
e
a ch
m
bone
cranial circulation
cranial innervation
l
mi
n
ica
5-60
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).
30. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).
32. Early-warning signals for sudden deterioration of diseases
large fluctuations in
cerebreal blood
flow control
DNB
B
DN
Migraine generator network (MGN)
bone
cerebral blood flow
?
Which
subnetworks
drive the
transtions into
the pain
phase?
highly variable
pattern of free
energy stravation
prodrome
aura
headache
postdrome
1 day
5-60min
4-72h
1 day
cortex
subcortical
parasympathetic
control
ON
OFF
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).
cranial innervation
spreading
depression
(SD)
&
brainstem
modulatory network
Dynamical network biomarker (DNB)
33. Unitary hypothesis for multiple natural migraine triggers
light
bone
cerebral blood flow
exercise
foods (chocolate, wine, ...)
menstrual cycle
olfactory stimuli
cortex
subcortical
parasympathetic
control
...
All triggers originate or activate subnetwork: pre- and
postganglionic parasym- pathetic neurons in the
SPG
SSN
ON
OFF
superior salivatory nucleus (SSN) and sphenopalatine
ganglion (SPG).
R. Burstein and M. Jakubowski, Unitary hypothesis for multiple triggers of the pain and strain of migraine. J Comp
Neurol. 493,9-14 (2005).
cranial innervation
sleep deprevation
brainstem
modulatory network
stress
34. Causality confusion in migraine
pain phase
prodromal phase
attack-free interval
time
τ
Hougaard et al, Provocation of migraine with aura using natural trigger factors, Neurology 80,428-431 (2013)
• M.A. Dahlem, J. Kurths, A. May, K. Aihara, M. Scheffer, and M. D. Ferrari, Causality confusion in migraine: ,
Cephalalgia accepted
35. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion
36. Modeling pain initiation and sensitization
50
seizure-like
afterdischarges
V
EK
dominance
pump current
ENa
0
Iapp
depolarization block
50
100
transmembrane
b
voltage (mV)
inside cell
outside cell
towards genetics
a
c
I
II
III
IV
m-gate
begin
deactivation
INa -driven
repolarization
V
+
0
5
10
15
20
time (s)
25
30
VI
35
cortical tissue
d
bone
cranial circulation
cranial innervation
cortex
cortex
HY,TH
SD
ignition
PAG
HY,TH
HY,TH
behavior,
sensory
processing
SD
corticothalamic
action
PAG
SPG
f g
bone
cranial circulation
cranial innervation
cortex
SD
release
noxious
agents
PAG
SPG
e
bone
cranial circulation
cranial innervation
SPG
visual aura (0min)
LC
LC
SSN
RVM
off
TCC
on
LC
SSN
RVM
TG
off
on
TCC
• Dahlem et al. (2013) Translational Neuroscience, 4, 282
SSN
RVM
TG
off
TCC
on
TG
sensory aura (15min)
37. From HH-type conductance-based to
conductance- & ion-based models (2nd generation model)
C
Extracellular Space
Cl
K+
-
Cl
K+
-
Na+
Na+
Neuron
3Na+
∂V
= −INa − IK − Ileak −Ipump −Iapp (1)
∂t
INa = gNa m3 h(V − ENa )
¯
IK
Ileak
= gK n4 (V − EK )
¯
= gleak (V − Vrest )
Diffusion
2K+
K+
Bath/Vasculature
∂n
∂t
∂[ion]o
∂t
∂[ion]i
∂t
= αn (1 − n) − βn,
A
Iion
FVolo
A
Iion
FVoli
∂h
· · · (2) − (4)
∂t
= −
=
(5) − · · ·
• N. H¨bel, E. Sch¨ll, M. A. Dahlem, Bistable dynamics underlying excitability of ion homeostasis in neuron
u
o
models under review
38. name
Cm
α
voltot
rn
A
Γ
R
T
F
Ipmax,1
Ipmax,2
gNamax
gKmax
gNal
gKl
gCl
ECl
value & unit
1µF/cm2
0.2
4/3π53 µm3
−15 3
√ 0.5236 × 10 m
3
5 1 − αµm≈4.6416µm
2
4πrn ≈ 270.73424µm2
≈ 2.7 × 10−6 cm2
A (αvoltot )−1 F−1
0.06698725858
8.3144621 JK−1 mol−1
293.5K
96 485.3415 sA/mol
5.14µA/cm2
matched Ipmax,1 at rest
120 mS/cm2
36 mS/cm2
0.12 mS/cm2
0.001 mS/cm2
0.5 mS/cm2
-65mV
description
conductance
volume fraction of ECS
total volume
total volume in m3
radius neural compartment
surface area
surface are in cm2
conversion factor
num. value (for given α, rn )
gas constant
temperatur
Faraday constant
pump rate
pump rate
conductance
conductance
leak conductance
leak conductance
leak conductance
initial reversal potential
39. FHM3 and spreading depression
60
V
EK
wild-type
20
V / mV
ENa
20
60
100
140
100%
20%
60
V
EK
mutant
20
V / mV
ENa
20
60
100
140
100%
20%
0
20
40
t/ s
60
80
100
• M.A. Dahlem, J. Schumacher, N. H¨bel, Linking a mutation in familial hemiplegic migraine type 3 to its
u
phenotype in spreading depression (in preparation)
40. FHM3 and action potential
40
40
oscillatory
wild-type
V / mV
HB2
50
70
0
50
40
60
excitatory
HB1
70
0
70
0
40
50
40
oscillatory
stable FP
unstable FP
30
100
150
Iapp / µ A cm−2
200
mutant
V / mV
HB2
50
70
0
50
40
60
excitatory
HB1
70
0
70
0
50
stable FP
unstable FP
30
100
Iapp / µA cm−2
150
200
• M.A. Dahlem, J. Schumacher, N H¨bel, Linking a mutation in familial hemiplegic migraine type 3 to its
u
phenotype in spreading depression (in preparation)
41. Multiscale disease: From molecules to entire brain
Functional mutations
Spreading depression (SD)
during a migraine attack
(e.g. FHM2: sodium-potassium pump)
cf.: Maagdenberg, et al., Ann. Neurol., 67 2010
Tottene, et al., Neuron, 61 2009
Atlas of Migraine and Other Headaches, Silberstein
Freilinger, et al. Nature Genetics 44 2012
et al (Editors)
42. Multiscale disease: From molecules to entire brain
Functional mutations
Spreading depression (SD)
during stroke
Subarachnoid space
Arachnoid
Ruptured
aneurysm
Dura mater
Blood clot
Arteriole
Neocortex
(e.g. FHM2: sodium-potassium pump)
Glutamate
K+
O2
Glucose
Delayed ischemic lesions
Energy
failure
Katie Vicari
Spreading
depolarization
Vasoconstriction
Microemboli
cf.: Maagdenberg, et al., Ann. Neurol., 67 2010
Tottene, et al., Neuron, 61 2009
Iadecola, ”Killer waves ...” Nature Medicine 15
Freilinger, et al. Nature Genetics 44 2012
(2009)
43. Neural dynamics during anoxia
membrane potential in mV
60
Wild-type
0
-60
60
Mutant
0
-60
24
28
32
36
40
time in s
van Rijn CM, et al. (2011) Decapitation in rats: latency to unconsciousness and the ‘wave of death’.
PLoS One 6, e16514.
Zandt B-J, et al. (2011), Neural Dynamics during Anoxia and the “Wave of Death”.
PLoS ONE 6, e22127.
Dichgans M, et al. (2005) Mutation in the neuronal voltage-gated sodium channel SCN1A in familial hemiplegic
migraine. Lancet 366, 371.
44. Neural dynamics during anoxia
membrane potential in mV
60
Wild-type
0
-60
60
Mutant
0
-60
24
28
32
36
40
time in s
van Rijn CM, et al. (2011) Decapitation in rats: latency to unconsciousness and the ‘wave of death’.
PLoS One 6, e16514.
Zandt B-J, et al. (2011), Neural Dynamics during Anoxia and the “Wave of Death”.
PLoS ONE 6, e22127.
Dichgans M, et al. (2005) Mutation in the neuronal voltage-gated sodium channel SCN1A in familial hemiplegic
migraine. Lancet 366, 371.
45. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion
46. Old problems remain
¨
“Uber die physiologischen Wirkungen der elektrischen B¨der liegen eine Reihe von Angaben [...] vor.
a
[...]
Im allgemeinen haben faradische B¨der einen erfrischenden Einfluß, galvanische sollen m¨de machen.
a
u
Es kommt f¨r die Wirkung entschieden auf die Dauer der B¨der an, k¨rzere werden mehr anregend, l¨ngere mehr
u
a
u
a
erschlaffend wirken.
Durchsichtig ist jedenfalls die physiologische Begr¨ndung dieser B¨der durchaus nicht, man wird sich vorstellen,
u
a
daßsie im allgemeinen die eines indifferenten Bades, mit dem ein milder Hautreiz verbunden ist, haben.
Es m¨gen dadurch Aenderungen in unseren Allgemeingef¨hlen, also Wohlbehagen, Erfrischung oder M¨digkeit
o
u
u
bedingt werden. Nach meiner Ansicht liegt aber die Hauptwirkung dieser elektrischen B¨der in erster Linie auf
a
suggestivem Gebiete, und das rechtfertigt ihre Anwendung und ihre unleugbaren Erfolge auf dem Gebiete der
nerv¨sen Allgemeinleiden, wie Hysterie, Neurasthenie etc.”
o
(Lehrbuch der klinischen Hydrotherapie, Max Matthes)
47. Feedback control of spreading depression (Talk 5. Feb!)
From bench
to bedside
!
48. Cooperation with Stephen Schiff Bruce Gluckman
Dept. Biomedical Engineering, Penn State (CRCNS)
Courtesy Neuralieve
Feedback control with Kalman filter
TMS (external forcing)
49. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).
50. Two tipping points
large fluctuations in
cerebreal blood
flow control
DNB
NB
D
Migraine generator network (MGN)
bone
cerebral blood flow
?
Which
subnetworks
drive the
transtions into
the pain
phase?
highly variable
pattern of free
energy stravation
prodrome
aura
headache
postdrome
1 day
5-60min
4-72h
1 day
cortex
subcortical
parasympathetic
control
ON
OFF
cranial innervation
spreading
depression
(SD)
brainstem
modulatory network
Dynamical network biomarker (DNB)
51. Modeling pain initiation and sensitization
50
seizure-like
afterdischarges
V
EK
dominance
pump current
ENa
0
Iapp
depolarization block
50
100
transmembrane
b
voltage (mV)
inside cell
outside cell
towards genetics
a
c
I
II
III
IV
m-gate
begin
deactivation
INa -driven
repolarization
V
+
0
5
10
15
20
time (s)
25
30
VI
35
cortical tissue
d
bone
cranial circulation
cranial innervation
cortex
cortex
HY,TH
SD
ignition
PAG
HY,TH
HY,TH
behavior,
sensory
processing
SD
corticothalamic
action
PAG
SPG
f g
bone
cranial circulation
cranial innervation
cortex
SD
release
noxious
agents
PAG
SPG
e
bone
cranial circulation
cranial innervation
SPG
visual aura (0min)
LC
LC
SSN
RVM
off
TCC
on
LC
SSN
RVM
TG
off
on
TCC
• Dahlem et al. (2013) Translational Neuroscience, 4, 282
SSN
RVM
TG
off
TCC
on
TG
sensory aura (15min)
52. Twist: A ‘ghost’ phathological state (waves)
d
postdrome
ictus
ictus
ictal
• Dahlem et al. (2013) Translational Neuroscience, 4, 282
f
+ aura
g chronification
ictus
c
ictus
interictal
ictus
a
prodrome
normal state
e
ictus
b
episodic manifestation
ictus
disease state
53. Phase-dependend neuromudulation
sensory innervation
blood
arachnoid
pia
cortex
SD
large MIA
blood
arachnoid
SD
small MIA
pia
cortex
depleted surface area
bone
dural sinuses
dura
5
y
IP: ignition phase AP: acute phase
x
a
MIA
4
b
3
c
2
d
1
0
e
f
slow dynamics
0
5
10
15
20
25
30
time
cf. Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
cf. Charles AC, Baca SM., Cortical spreading depression and migraine. Nat Rev Neurol. 9:637-44, (2013)
• M. A. Dahlem and T. Isele: Transient localized wave patterns and their application to migraine. J. Math.
Neurosci. 3,7 (2013).
35
54. Phase-dependend neuromudulation
sensory innervation
blood
arachnoid
pia
cortex
SD
large MIA
blood
arachnoid
SD
small MIA
pia
cortex
depleted surface area
bone
dural sinuses
dura
5
y
IP: ignition phase AP: acute phase
x
a
MIA
4
IP Stim.
b
AP Stim.
3
c
2
d
1
0
e
f
slow dynamics
0
5
10
15
20
25
30
time
cf. Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
cf. Charles AC, Baca SM., Cortical spreading depression and migraine. Nat Rev Neurol. 9:637-44, (2013)
• M. A. Dahlem and T. Isele: Transient localized wave patterns and their application to migraine. J. Math.
Neurosci. 3,7 (2013).
35
55. Phase-dependend neuromudulation
IP: ignition phase AP: acute phase
bone
sensory innervation
blood
arachnoid
any node in the
migraine generator
network is potential
target for
neuromodulation
pia
cortex
large MIA
blood
a
CC
aura
b
hypermia
HY,TH
oligemia +
CTX
HY,TH
vlPAG
vlPAG
SPG
LC
SuS
off
on
x
a
MIA
4
IP Stim.
b
AP Stim.
3
c
2
d
on
TG
0
e
f
slow dynamics
SuS
off
TCC
y
1
RVM
TG
5
SPG
LC
RVM
TCC
CC
pain
CTX w loc SD
depleted surface area
dural sinuses
dura
0
5
10
15
20
25
30
time
cf. Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
cf. Charles AC, Baca SM., Cortical spreading depression and migraine. Nat Rev Neurol. 9:637-44, (2013)
• M. A. Dahlem and T. Isele: Transient localized wave patterns and their application to migraine. J. Math.
Neurosci. 3,7 (2013).
35
58. Various SD patterns cause different migraine types?
a
pain onset
5 min
~20 min
~60 min (full-scale aura)
MA
TAA
MIA
aura
MO
MIA
TAA
b
• M. A. Dahlem et al., Spreading depression in migraine without aura: a model-based hypothesis. (in preparation)
59. Various SD patterns cause different migraine types?
total area affected (TAA)
exct. duration (ED)
1k
4
2
(dotted)
1
1
1
4
2
1
0
1
0
2k
0
1k
MWoA
MWA
−1
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
maximal instantaneous area (MIA)
0.8
1
MWA
aura threshold
MWoA
MWoA MWA
1cm
large
TAA
MIA
pain
aura
IA
correlation
3
2
2
w/o
headache
pain threshold
0.5
MxWA
smooth histogram (solid lines)
mean STD
2k
3
classification
#
1
0
total affected area (TAA)
• M. A. Dahlem et al., Spreading depression in migraine without aura: a model-based hypothesis. (in preparation)
60. Individual ‘hot spots’ and ‘labyrinth’ determine attack
e
iv
sit
po
ne
ga
t
ive
Principles
Validate
• simulations on simpler shapes
• analytical results with isothermal
• uploading patient’s MRI scanner readings
• finite element analysis
coordiantes (toroidal coordinates)
• polygon mesh processing
61. Excitation waves on curved surfaces
Paradigmatic SD model on gyrified cortex.
∂u
∂t
∂v
∂t
1
1 ∂
= u − u 3 − v + Du √
3
g ∂αi
=
√ ∂u
gij g i
∂α
(u + β)
SD in weakly excitable cortex posses critical properties.
First approximation: localized SD follows shortest path.
62. Outline
Electrical magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion
68. Modern neuromodulation
”The headache future is bright for neuromodulation techniques ... if we
manage to understand how they work” (Jean Schoenen)
69. Models fill the ‘gaps’ in the multiscale framework
seizure-like
afterdischarges
dominance
pump current
ENa
0
Iapp
depolarization block
50
100
c
V
EK
II
III
10
15
20
time (s)
cortex
HY,TH
V
25
30
35
balanced excitation and
inhibition in ion-based models
VI
e
behavior,
perception
sensory
processing
SD
corticothalamic
action
PAG
SPG
visual aura (0min)
LC
m-gate
begin
deactivation
INa -driven
repolarization
5
bone
cranial circulation innervation
release noxious agents
IV
+
0
d
I
organ level
50
transmembrane
cellular level
outside cell
inside cell
molecular level
genetics
b
voltage (mV)
a
RVM
off
on
SSN
TG
TCC
sensory aura (15min)
(a) Functional mutations, either FHM, CADASIL, ... or GWAS.
(b) Hodgkin-Huxley type, single cell electrophysiology models.
(c) Neural mass/fields population models, with subpopulations
having specific synaptic receptor distribution.
(d) Local circuits, in particular including the migraine generator
network in the brainstem
(e) Aura symptoms, mental dysfunctions, impared sensory and
cognitive processing
70. Recent papers
M.A. Dahlem, J. Kurths, A. May, K. Aihara, M. Scheffer, and M. D.
Ferrari, Causality Confusion in Migraine Cephalalgia, (accepted).
M. A. Dahlem, Migraines and Cortical Spreading Depression,
Encyclopedia of Computational Neuroscience, Springer. (accepted)
M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J.
Kurths, Towards dynamical network biomarkers in neuromodulation of
episodic migraine, Translational Neuroscience, 4,282-294 (2013).
M. A. Dahlem: Migraine generator network and spreading depression
dynamics as neuromodulation targets in episodic migraine. Chaos, 23,
046101 (2013).
M. A. Dahlem and T. Isele: Transient localized wave patterns and their
application to migraine. J. Math. Neurosci. 3,7 (2013)
J. P. Dreier, T. Isele, C. Reiffurth, N. Offenhauser, S. A. Kirov, M. A.
Dahlem, and O. Herrars: Is spreading depolarization characterized by an
abrupt, massive release of Gibbs free energy from the human brain
cortex? The Neuroscientist 19,25-42 (2012).
M. A. Dahlem and J. Tusch: Cortical magnification tensor predicts a
virtual visual streak in humans waves, J. Math. Neurosci. 2,14 (2012)
71. Manuscripts in preparation
N. H¨bel, E. Sch¨ll, and M. A. Dahlem, Bistable dynamics underlying
u
o
excitability of ion homeostasis in neuron models (revised and under
review, 14 pages, 7 figures, 3 tables, ms on arxiv)
F. Kneer, E. Sch¨ll, and M.A. Dahlem, Nucleation of reaction-diffusion
o
waves on curved surfaces. (submitted, 23 pages, 11 figures, 4 movies)
M. A. Dahlem, F. Kneer, E. Sch¨ll, B. Schmidt, I. Bojak, and J. Kurths,
o
Personalized treatment strategies in episodic migraine by
neuromodulation devices. (12 pages, 5 figures, 1 movie)
M. A. Dahlem, Julia Schumacher, N. H¨bel, Linking a mutation in
u
familial hemiplegic migraine type 3 to its phenotype in spreading
depression, 4 figures, 8 pages
F. Kneer, K. Obermayer, M. Dahlem, Analyzing critical propagation in a
reaction-diffusion-advection model using unstable slow waves.
(submitted)
M. A. Dahlem, et al. Spreading depression in migraine without aura: a
model-based hypothesis. (in preparation)
72. Conclusions
We need more non-invasive
imaging data of migraine with aura
to test predictions.
Sef-organizing patterns provide a
unifying concept including silent aura,
migraine w or w/o headache/aura
Dynamical cocepts may refine
neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine
Visual hemifield
Primary visual cortex
1 cm
27 min
10°
25
23
21
1
3
5
7
17
15
19
73. Conclusions
Sef-organizing patterns provide a
unifying concept including silent aura,
migraine w or w/o headache/aura
Dynamical cocepts may refine
neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine
(1)
(2)
no attack
MWoA
(a)
cortex
top view
y
(3)
MWA
x
(4)
to ta l a ff e cte d a re a TAA
We need more non-invasive
imaging data of migraine with aura
to test predictions.
50 (1)
(2)
(3)
25
(4)
(b)
above
pain
threshold
6.25
time
0 3 6 9 12 15 18 21 24 27
0
2.5
6.25
maximal instantaneous area MIA
74. Conclusions
We need more non-invasive
imaging data of migraine with aura
to test predictions.
Sef-organizing patterns provide a
unifying concept including silent aura,
migraine w or w/o headache/aura
Dynamical cocepts may refine
neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine
75. Cooperation Funding
Frederike Kneer, Niklas H¨bel, Julia
u
Schumacher, Thomas Isele
Paul Van Valkenburgh, Bernd Schmidt
Nouchine Hadjikhani
(Martinos Center for Biomedical Imaging, MGH)
Steven Schiff
berlin
(Penn State Center for Neural Engineering)
Andrew Charles
(Headache Research and Treatment Program, UCLA School of
Medicine)
Jens Dreier
(Department of Neurology, Charit´; University Medicine, Berlin)
e
Klaus Podoll
(University Hospital Aachen)
Migraine Aura Foundation
76. Mainly two neural theories of migraine
”Migraine generator”-theory
S1
SMA
PPC
ACC
Th
PFC
Amyg
Insula
PAG
”Spreading depression”-theory
77. SD: Wave of massive ionic imbalance
(mM)
Ve
+
Na
log [cat] , M
150
60
50
+
Na
+
-1
K
Ca++
3
1.5
0.08
-2
+
0 10 20 30 s
K
-3
-4
-7
Ca++
+
H
-8
20 mV
Ve
unit
act.
1 min
Lauritzen (1994) Brain 117:199.
78. SD does not curl-in in human cortex
10 min
1cm
Only about 2-10% but not 50% cortical surface area is affected!
right: modified from Hadjikhani et al. PNAS 98:4687 (2001).
• Dahlem Hadjikhani, PLoS ONE, 4: e5007 (2009).
79. SD does not curl-in in human cortex
SD curls in to form
spirals with T=2.45min!
spiral
core
1cm
10 min
1cm
Only about 2-10% but not 50% cortical surface area is affected!
right: modified from Hadjikhani et al. PNAS 98:4687 (2001).
• Dahlem Hadjikhani, PLoS ONE, 4: e5007 (2009).
• Dahlem M¨ller, Exp. Brain Res. 115,319, (1997).
u
80. Re-entrant SD waves with functional block
Z-type rotation causes a wave break in the spiral core.
Dahlem M¨ller (1997) Exp. Brain Res. 115:319
u
81. Re-entrant SD waves with anatomical block
Reshodko, L. V. and Bureˇ, J Biol. Cybern. 18,181 (1975)
s
84. Transient times in flat and curved geometry
torus, without control
torus, with control
flat, without control
30
∂R∞
50
ring
40
outside
20
S
torus outside
S
30
with control
without control
wave
inside
flat
20
torus inside
outside
10
inside
10
0
1.3
1.32
1.34
β
1.36
1.38
0
0
10
20
30
40
t
50
60
70
80
92. Cerebral blood flow in migraine
Radionuclide xenon 133 method, used to image brain’s blood flow
Olesen, J. , Larsen, B. and Lauritzen, M., Focal hyperemia followed by
spreading oligemia and impaired activation of rCBF in classic migraine, Ann.
Neurol. 9, 344 (1981)
95. fMRI patterns is more diffuse than SD patterns
end (min 30)
start (min 20)
reference (min 0)
modified from Hadjikhani et al. (2001) PNAS 98
96. fMRI patterns is more diffuse than SD patterns
end (min 30)
start (min 20)
reference (min 0)
What if the the blood flow provides a
long-range or global negative feedback?
modified from Hadjikhani et al. (2001) PNAS 98
98. ”Migraine generator” in the brainstem
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day
99. A conductor of a neural orchestra playing migraine
70%
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day
100. A conductor of a neural orchestra playing migraine
rarely
(but: unreported cases)
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day
101. A conductor of a neural orchestra playing migraine
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day
103. Common etiology or 2 mechanisms in MWoA and MWA?
heightened
susceptibility
trigger
SD
prodrome
aura
delayed trigger
headache
1. Only one upstream trigger?
2. MWoA MWA share same pain phase? 3. Silent aura? 4. Even prevalent?
5. Delayed headache link? 6. Missing the pain phase?
SD: Spreading Depression, see next slide
104. Unified Minimal (4D) Model of
Spiking, Seizures and Spreading Depression
e xtra c e llula r pota s s ium
pe riodic SD
uns ta ble lim it c yc le
s ta ble e q uilibrium
70
60
Kex,max in mMol/ l
50
40
30
20
TR?LP
LP
HB
TR
10
LP?
HB
0
4
6
8
10
14
12
Kbath in mMol/ l
16
18
20
22
105. Unified Minimal (4D) Model of
Spiking, Seizures and Spreading Depression
m e m bra ne pote ntia l
60
LP?
40
TR
Vmax in mVolt
20
0
ENa
V
0
20
EK
-100
LP
1min
HB
40
LP
HB
HB
LP
HB LP
TR?
60
80
4
6
8
10
14
12
Kbath in mMol/ l
16
18
20
22
107. Excitable media – Traveling wave solutions
Canonical RD eqs.
(in weak limit, β large but not too large)
∂t u = f (u) − v +
∂t v
= ε(u + β)
2
u
108. Excitable media – Traveling wave solutions
Canonical RD eqs.
(in weak limit, β large but not too large)
∂t u = f (u) − v +
∂t v
2
u
= ε(u + β)
Schenk et al. Phys. Rev. Lett. 78, 3781 (1997)
109. Excitable media – Traveling wave solutions
Canonical RD eqs.
(in weak limit, β large but not too large)
∂t u = f (u) − v +
∂t v
2
traveling
wave
u
= ε(u + β)
sup
sh
sh
o
st
ld imula
t
50
40
io
n
wave size S
hre
sub-thre
∂R∞
60
er-t
s
old
30
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
20
10
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4
110. Excitable media – Traveling wave solutions
traveling
wave
Canonical RD eqs.
(in weak limit, β large but not too large)
su
ol
es h
- th r
p er
sub-thre
n
= ε(u + β)
sub-excitable
wave size S
50
40
30
20
10
0
1.3
1.32
1.34
1.36
threshold β
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
∂R∞
60
ti o
∂t v
u
o
st
ld imula
∂t u = f (u) − v +
2
sh
ds
1.38
1.4
111. Excitable media – Traveling wave solutions
traveling
wave
Canonical RD eqs.
(in weak limit, β large but not too large)
su
ol
es h
- th r
p er
sub-thre
n
= ε(u + β)
∂P1D
30
20
not excitable
sub-excitable
wave size S
50
40
10
0
1.3
1.32
1.34
1.36
threshold β
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
∂R∞
60
ti o
∂t v
u
o
st
ld imula
∂t u = f (u) − v +
2
sh
ds
1.38
1.4
112. Excitable media – Traveling wave solutions
traveling
wave
Canonical RD eqs.
(in weak limit, β large but not too large)
su
ol
es h
- th r
p er
sub-thre
n
= ε(u + β)
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
∂R∞
60
ti o
∂t v
u
o
st
ld imula
∂t u = f (u) − v +
2
sh
ds
∂P1D
40
30
20
not excitable
sub-excitable
wave size S
50
10
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4
critical
nucleation
117. Minimum threshold in a flat geometry
∂R∞
60
wave size S
50
ring
40
30
∂P1D
wav
e
torus outside
1
torus inside
1
20
10
1
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4
118. Minimum threshold in a flat geometry
∂R∞
60
wave size S
50
ring
40
30
wav
e
∂P1D
2
torus outside
20
2
10
1
1
torus inside
1
2
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4
119. Migraine scotoma reveal functional properties
Pattern matching
A
B
4
7
13
C
9
• Dahlem Tusch, J. Math Neuroscie. 2,14 (2012)
120. Migraine scotoma reveal functional properties
Pattern matching
”Curved” retinotopic mapping
A
B
a
ÙÒ Ù×
Ð Ò Ù Ð ÝÖÙ×
13
9
Ë
C
b
c
m
• Dahlem Tusch, J. Math Neuroscie. 2,14 (2012)
Ú
Ð
e
4
7
d
m
Ù
½¼Æ