Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**
Consortium leader
PETER PAZMANY CATHOLIC UNIVERSITY
Consortium members
SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER
The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***
**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben
***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.
ELECTROPHYSIOLOGICAL METHODS OF THE STUDY OF THE NERVOUS- AND MUSCULAR SYSTEM
LECTURE 9
PROCESSES RESPONSIBLE FOR GENERATION OF BRAIN BIOELECTRIC SIGNALS
Az ideg- és izomrendszer elektrofiziológiai vizsgálómódszerei
(Agyi bioelektromos jelek létrejöttéért felelős folyamatok)
BRAIN BIOELECTRIC SIGNALS
• Electric signals from the brain can be recorded via different types of electrodes:
scalp EEG electrodes, ECoG electrodes placed on cortical surface or implantable electrodes recording from the brain tissue.
• These recorded signals can provide valuable information about brain function and pathology.
• Care must be taken while interpreting these signals: signal waveform and other parameters depend on several factors.
• These factors can be: electrode parameters, recording setup parameters, brain- electrode junction characteristics, brain cellular structure.
• In this lecture we shall discuss the electric signal generators of the brain.
BRAIN ELECTRIC SIGNALS RECORDED ON SCALP
• Scalp electrode recordings are common because they are non-invasive and relatively easy to carry out.
• Problems:
• Skull filters the recorded signal.
• Scalp electrodes record the summated activity of millions of neurons.
• In order to determine the exact source of recorded signals these signals have to be separated based on their different generators.
• This is not an easy and trivial task due to the enormous number of cells located in the brain.
• To extract this information from recorded signal first the underlying cellular mechanisms must be understood.
CELLULAR SOURCES OF BRAIN ELECTRIC SIGNALS
Schematic image of a tetrode inserted into cortical tissue. Tetrodes are powerful tools to record single unit signals to be effectively sorted later. As seen on image, even a small volume of cortical tissue contains plenty of neurons that contribute to the recorded electric signal. In this case triangulation helps to determine the position of recorded
neurons. Similar methods can be used for EEG recordings to be discussed later.
1mm3 cortical tissue:
~ 105neurons
~ 109 synapses
~ 10.000 synapses/neuron (Stevens, 1989)
Conclusion: Only by studying single units the brain electrical activity cannot be understood.
G. Buzsáki, Large-scale recording of neuronal ensembles, Nature neuroscience, Vol. 7, No. 5. (May 2004), pp. 446-451
TWO TYPES OF ELECTRICAL ACTIVIY OF THE NEURONS
• The nerve impulse (action potential) is an all or none type response that is conducted along the axon. It is generated if the membrane potential reaches a
threshold depolarization at the axon hillock. The action potential can be regarded as a digital signal, the code is the number or timing of the impulses.
• Subthreshold membrane potential changes are induced by excitatory and inhibitory synaptic processes. Contrary to the action potentials the postsynaptic potential
changes induced by synaptic currents are analog signals, they are summated both in time and space. The time course of the action potential is short (0,5-3 ms), the
duration of the postsynaptic potentials are much longer (10-100 ms). (see L. 3-4.)
• Because of the electric properties of the brain tissue the action potentials do not spread long distance in the extracellular space. In the genesis of the EEG type brain
SYNAPTIC MEMBRANE CURRENTS
• During communication between neurons two types of postsynaptic currents can occur: excitatory and inhibitory.
• In both cases current flows through the membrane. The extracellular medium, the membrane and the intracellular space form a circuitry so all the membrane currents together must complete circuit loops.
• At excitatory synapses ion current flows into the cell so the membrane acts as an active sink. To complete the loop, further parts of the membrane act as passive sources.
• At inhibitory synapses ion current flows out from the cell so the membrane acts as an active source. To complete the loop further parts of the membrane act as passive sinks.
SYNAPTIC MEMBRANE CURRENTS
SCHEMATIC MODEL OF NEURONAL MEMBRANE CIRCUITRY
The schematic shows the model of the extracellular medium – membrane –
intracellular space circuit. Note the closed loop of the components realized by the
active current source and the passive current sink parts of the membrane.
Ra: intracellular resistance Re: extracellular resistance Rm: membrane resistance
POTENTIAL SOURCE MODEL OF NEURON
• According to the previous schematic there is charge distribution along the
pyramidal neuron membrane: one pole is the active membrane part, the other is the passive, extra and intracellular loop completing membrane part.
• In a general view these membrane sections can be seen as two, opposite charged point charges, generating potential fields around them.
• To sum up, the discharged neuron can be modeled as a single dipole that generates potential field around itself.
• The axis of generator dipole is always vertical, somatic and dendritic axes of pyramidal cells in the cerebral cortex are always perpendicular to the cerebral surface.
• The charge distribution of this model also follows the real situation in cortex:
charge is distributed along the dendritic and somatic axis of neurons.
FIELDS INDUCED BY MEMBRANE CURRENTS
• All currents (membrane or any other type) induce electric and magnetic fields.
• These fields are always perpendicular to each other according to electromagnetic laws.
• The induced fields can be measured by appropriate recording instruments.
• Extracellular potential fields induced by synaptic currents can recorded by electrodes, e. g. surface EEG electrodes.
• Magnetic fields induced by synaptic currents can be recorded by MEG recording setups.
• Since the two types of induced fields are perpendicular to each other during the design of recording setups this fact has to be taken in account.
FIELDS INDUCED BY MEMBRANE CURRENTS
Electric field Magnetic field
FIELDS INDUCED BY NEURONAL POPULATIONS
• Since in most cases activity of a larger neuronal population is recorded, it is necessary to consider how these populations induce electric fields in the extracellular space.
• The characteristics of induced fields largely depend on the spatial organization of the generating neuronal population.
• Pyramidal neurons in the neocortex form a row with their cell bodies and parallel apical dendritic processes. This formation induces a so-called open field. The term open field is used because the parallel formation lets individual electric fields to summate and propagate undisturbed or uninterfered.
• In many cases, neuron cell bodies are packed together and dendritic arborization distributed radially. In this case, electric field cannot propagate uninterfered, so this formation is called closed field.
• In most cases, some neurons are parallel while others are packed together. The field induced by such a population is called open-closed field.
FIELDS INDUCED BY NEURONAL POPULATIONS
OPEN FIELD CLOSED FIELD OPEN-CLOSED FIELD
DIPOLE MODEL FOR CELL POPULATIONS
• The previously introduced dipole model is not only useful for single cells but also for whole neuron populations.
• The electrical field of the population in three dimensional space can be substituted by a single dipole located in the center of gravity of a neuron population.
• The charge of this dipole is the vector sum of charges of all neurons in population.
• The substituting dipole of the neuron population is called the equivalent dipole of the population.
• In this sense, the previously described population-induced fields can also be described as single dipoles instead of complicated structure neuron populations.
• This is a powerful tool to model generators of discharges recorded with brain electrodes.
SCHEMATIC OF EQUIVALENT DIPOLE MODEL
Randomly distributed dipoles in a neuron
population
Equivalent dipole of the population
DIRECTION OF EQUIVALENT DIPOLE
• Direction of single pyramidal neuron dipoles in the top of a neocortical gyrus is perpendicular to skull surface: this direction is called radial dipole.
• An equivalent dipole is also radial if its axis is perpendicular to the skull surface.
• However, about 2/3 of the cortex is folded: these cortical layers are in sulci thus not parallel with skull surface.
• Although dipoles located in these sulci are also perpendicular to the cortical surface, they are not perpendicular to skull surface therefore they cannot be assumed as radial dipoles.
• As a consequence their generated field appears differently on brain electric recordings.
• If dipole is located on border of surface and a sulcus it is called oblique dipole.
• If it is located in the sulcus it is called tangential dipole.
SCHEMATIC OF EQUIVALENT DIPOLE DIRECTIONS
Tangential dipole
Oblique dipole
Radial dipole
POTENTIAL DISTRIBUTION ON THE SCALP
• Equivalent dipoles generate potential fields that can be recorded on scalp.
• Recorded potential distribution depends on several different factors:
• Direction of dipole influences recorded signal:
• Radial dipoles appear as potential field locally.
• Tangential dipoles induce electrical potential field on the scalp distantly.
• Size of source also influences recorded signal: few dipoles generate only slight potential difference that can barely be detected by scalp EEG electrodes. Large volume of dipoles is needed to register their generated potential by scalp EEG electrodes.
• Depth of dipole influence: signal is attenuated rapidly with increasing distance therefore deep lying dipoles contribute slightly to scalp EEG waves.
SCALP POTENTIAL FIELDS DEPENDING ON DIPOLE DIRECTION
As can be seen in the following figures:
• Radial dipole: focus of potential field right over the source. Clearly radial dipoles can practically never be detected, however, only radial component of a dipole contributes to the recorded potential.
• Oblique dipole: focus of potential field slightly shifted over the contralateral hemisphere due to tangential component of dipole.
• Tangential dipole: Potential field completely smothered by its opposite sign pair.
Potential field focus shifted over contralateral hemisphere.
POTENTIAL FIELD OF RADIAL DIPOLE IN RIGHT
HEMISPHERE
POTENTIAL FIELD OF OBLIQUE DIPOLE IN RIGHT
HEMISPHERE
POTENTIAL FIELD OF TANGENTIAL DIPOLE IN
RIGHT HEMISPHERE
IMPORTANCE OF POTENTIAL DISTRIBUTION ON SCALP
• It is essential to know how different dipoles distribute potential on scalp because it makes recordings interpretable, comparable and repeatable.
• According to measurements, the decisive factors in potential distribution are direction and size.
• Two thumb-rules:
• The larger the number of generating dipoles is, the better the recorded signal amplitude.
• The more radial the source dipole is, the better the recorded signal amplitude.
• EEG electrodes have to be designed and distributed such that they are able to record
EEG DESIGN TO BEST FIT POTENTIAL DISTRIBUTION
• Standard 10-20 EEG electrode system is developed to give standard and
comparable EEG electrode recording coordinates independent of head size and shape.
• This makes possible to compare EEG results from different patients and to define reference points on scalp for comparison and source localization.
• However, this system is also effective in spanning over large areas of signal generators thus picking up as much signal as possible.
• In contrast, large spacing has poor resolution for small area source localization.
DETERMINING SOURCES OF RECORDED POTENTIAL FIELDS
• This is a so called inverse problem: the location and strength of potential sources have to be determined based on recorded potentials
• For comparison, forward problem would be determining potential distribution on scalp based on the sources located inside the brain
• Source localization is an ill-posed inverse problem, i. e. there is an infinite number of possible solutions for the problem
• This means that there are infinite variations of different intracranial potential source sets to generate exactly the same scalp recorded potential distribution
• Consequence: constraints must be put on the number, type, or location of sources in order to get a unique solution
• These constraints together are called source model
NON-UNIQUE SOLUTION FOR INVERSE PROBLEM
As seen on figure, two different source distributions can generate the very same recorded potential on scalp. This is why no unique solution for the inverse problem exist.
CHOOSING THE RIGHT SOLUTION FOR INVERSE PROBLEM
• Since there is no unique solution for the inverse problem, there is no correct solution for it
• There are only better and worse solutions that are closer to or further from the real biological source distribution
• Mathematical methods were developed to find best possible solution. Best possible means the closest solution to the real biological source distribution
• Types of methods:
• Model-dependent: constraints are put on some source parameters, e. g. number, type or location. These methods can be subdivided into linear and non-linear methods.
• Model independent: no constraints on source parameters are put, source parameters are estimated by different mathematical interpolation methods
OTHER CONTRIBUTING FACTORS TO SOURCE LOCALIZATION PROBLEMS
• Apart from non-uniqueness of solution for inverse problem there other contributing factors that make source localization more difficult
• Artifacts of recordings, e. g. muscle or eye movement artifacts may reduce signal quality and must be eliminated from signal before performing localization methods
• Noise of recording also reduces signal quality thus noise filtering or reduction is essential before source localization
• Voltage conductor parameters are also play an important role. While brain tissue and scalp have a relatively good conductivity, skull conductivity is low. This has to be taken into account in order to avoid source misplacement introduced by
conductivity differences
• To overcome this problem a three shell spherical head model is widely used, where the three shells are brain, skull and scalp. This model can compensate for
conductivity change introduced source localization errors.
• A more realistic head model can be introduced by finite element method
THREE SHELL SPHERICAL HEAD MODEL
MATHEMATICAL FORMULATION OF INVERSE PROBLEM
• The previously listed mathematical methods need a mathematical formulation of source localization inverse problem
• The formulation:
J=TΦ
• Where:
J: current density
T: inverse transformation matrix Φ: measured potential distribution
• T inverse transformation matrix is the inverse of forward problem transformation matrix
• Forward problem aims to determine scalp potential distribution based on brain potential source distribution represented by brain current density. The
transformation matrix contains head conduction parameters derived from a head model, e. g. three shell spherical head model
MODEL-DEPENDENT INVERSE PROBLEM SOLUTION METHODS
• These methods use a source model that means putting constraints on the source parameters: number, type, location
• Usually, these methods use one or more dipoles as sources
• To characterize a dipole six parameters are needed: three spatial coordinates and three dipole momentum vector coordinates which represent the direction of
potential induced by the dipole
• Non-linear methods use one or a few source dipoles with different ratio of predetermined dipole parameters
• Linear methods use many source dipoles distributed widely in the cortex with almost all dipole parameters determined
NON-LINEAR SOURCE LOCALIZATION METHODS
• The simplest method uses a single equivalent dipole and tries to fit all dipole parameters such that they fit to all measured potentials
• This is carried out with non-linear least-square minimization algorithm
• This method is sensitive to noise, artifacts, head model inaccuracies and also computationally demanding
• Similar models with more fixed parameters can be used:
o Fixed dipole model: it is assumed that the dipole has a fixed location and
orientation, only its strength varies within a given time window. Less sensitive to noise and artifacts.
o Rotating dipole model: only dipole location is assumed to be fix, both orientation and strength can vary within a given time window.
• All of these methods have the disadvantage that it is quite difficult to fit a single dipole to all recorded potentials.
NON-LINEAR SOURCE LOCALIZATION METHODS
• To overcome the problem of single dipole modeling additional dipoles can be added to the model
• Constraints have to be applied on the parameter search algorithm in order to avoid too close dipole locations or orientations
• In case of too closely located or oriented dipoles the least-square minimization algorithm is unable to reliably determine the individual dipole parameters
• Theoretical maximum for the number of added dipoles depends on the number of recording electrodes (M)
• Fixed dipole model: maximum number of electrodes is M-1
• Rotating dipole model: maximum number of electrodes is (M-1)/3
• When all dipole parameters must be estimated by parameter search algorithm (unconstrained model): maximum number of electrodes is (M-1)/6
APPLICATION OF NON-LINEAR SOURCE LOCALIZATION METHODS
• Clinical application: equivalent dipole modeling of epileptic spike potentials
• Location of one or more epileptogenic regions of cortex as well as epileptic spike propagation patterns can be determined using fixed or rotating dipole models
• Ictal discharges may also be analyzed in a similar fashion
• Used to differentiate mesial-basal temporal lobe foci (tangential and radial dipoles) from lateral neocortical or extratemporal foci (radial dipole)
• This provides useful information for evaluation of intractable epilepsy patients for possible epilepsy surgery
LINEAR SOURCE LOCALIZATION METHODS
• These methods assume larger number of source dipoles compared to non-linear methods. This means a couple of hundred dipoles in linear case and a couple of dozen dipoles in non-linear case.
• Location and orientation of dipoles are fixed, moreover, are part of the model and not the solution set, therefore only dipole strength must be estimated. Thus the potential on any scalp electrode is a linear combination of the individual dipole source strengths.
• Linear algebraic methods can be used to solve for these dipole source strength, therefore the name, linear methods.
• These methods are faster than non-linear methods since only linear operations have to be performed during solution
SUBGROUPS OF LINEAR METHODS
• From mathematical point of view, three subgroups of linear methods can be
defined, depending on the relation between the number of source dipoles (N) and the number of recording electrodes (M)
• N<M – fewer sources than electrodes: no exact match among the inverse problem solutions to recorded potential. Thus best solution is found similarly to non-linear methods: by least-square minimization. Example: FOCUS method – 16 radial sources, one or two located in each brain lobe and hemisphere
• N=M – equal number of sources and electrodes: one unique solution to the inverse problem. Example: spatial deconvolution algorithm – one radial dipole source located directly beneath each scalp electrode
• N>M – more sources than electrodes: infinite number of solutions to the inverse problem match the recorded scalp potentials exactly. The chosen best solution is the one minimum norm solution which minimizes the sum of the squares of the source dipole strengths. Examples: cortical imaging technique (CIT), low-resolution
electromagnetic tomography (LORETA)
FOCUS METHOD
• Developed by Michael Scherg in 1996 in Germany
• Uses time domain analysis in order to find multiple source dipoles
• Searches for single source dipole in a given time window and applies least-square minimization algorithm for the whole dataset
• More source dipoles are added in following time windows until the sources fit all recorded potentials
• Implemented in Brain Electrical Source Analysis (BESA) software
• BESA software displays good temporal resolution EEG signals combined with MRI images for better spatial resolution
• Further reading: http://www.besa.de
MINIMUM NORM METHOD
• Head model projected on a 3D grid. There are three pair wise perpendicular source dipoles in each grid point.
• The aim is to find the minimum energy (minimum current density) solution
• Mathematically, this is the minimum L2-norm solution:
• According to simulations, minimum norm solution tends to choose weak and local activation patterns and places deep-lying sources on the surface. The latter can be compensated by choosing appropriate weighting.
LORETA
• Low-resolution electromagnetic tomography
• Developed by Roberto Domingo Pascual-Marqui in 1994
• Constraint: the method looks for a smooth spatial solution
• Mathematically: minimizing the second derivative of the weighted sources, which means minimizing the Laplacian of the weighted sources
• Physiological reasons for spatially smooth solution: neighboring neurons are activated synchronously and change their orientation gradually
• Developed version: sLORETA – standardized low-resolution electromagnetic tomography
• sLORETA has no localization bias in the presence of measurement and biological noise
MODEL-INDEPENDENT INVERSE PROBLEM SOLUTION METHODS
• In contrast to model-dependent methods, model-independent methods do not need any assumptions about the number, type or configuration of sources in the brain
• Topographic display methods (brain mapping): these algorithms can interpolate potentials to intermediate points between the scalp electrode positions.
• There different types of topographic display methods: nearest neighbor inverse distance weighted, all-electrode inverse distance weighted, rectangular surface splines or
rectangular three-dimensional splines, spherical surface splines, spherical harmonic expansion, and single dipole or multidipole source model methods
• Laplacian methods, very similar to topographic display methods
• Multivariate statistical methods: principal component (PCA) and independent component (ICA) analyses may be used to decompose multichannel EEG epochs into multiple
linearly independent components. Can be used as a starting point for source localization techniques.
• Bayesian methods: used to introduce a priori information (e. g. source must be in the gray matter) into localization processes. Based on usage of probability distributions.
MAGNETOENCEPHALOGRAPHIC SOURCE LOCALIZATION
• Magnetoencephalography (MEG): recording of the small magnetic fields produced by electrical activity of neurons in the brain
• According to electromagnetism theory, magnetic fields are always perpendicular to their generating electric fields. Therefore, MEG is only sensitive to fields induced by tangential dipoles. In contrast, EEG is sensitive mostly to radial dipole induced fields.
• The great advantage of MEG compared to EEG from source localization point of view is that all structures between brain and recording setup are transparent to magnetic fields. Thus, magnetic fields reach detectors unattenuated, making
compensation for conductor induced distortions, seen in the case of EEG (e. g. the three shell spherical head model), unnecessary.
SIGNALS RECORDED WITH IMPLANTED ELECTRODES
• In the previous section signals recorded with scalp or brain surface electrode were discussed. The methods described are adapted to these conditions, e. g. skull and scalp conduction issues.
• However, brain electric signals recorded with implanted electrodes play an important role in research and clinical practice
• Implanted electrodes can record synaptic and action potentials
• Both synaptic and action potentials provide valuable information on brain functions
• However, synaptic potentials characterize spatial source distribution better
• The method used to analyze source distribution that generates recorded synaptic potentials is called current source density analysis
PROPERTIES OF SYNAPTIC POTENTIALS
• Synaptic potentials: under-threshold potentials that do not induce an action potential but can still be recorded with implanted electrodes
• Synaptic potentials play an important role in synaptic potentiation
• They are summed up in a huge volume and these summed potentials are recorded, called field potentials
• Recorded synaptic potentials do not contain volume conductor effects, e. g. skull induced distortion
• Current source density analysis aims to determine the sources and sinks of these synaptic potentials
• Current source density analysis gives an overview of the spatial distribution of synaptic potential generators
CURRENT SOURCE DENSITY (CSD) ANALYSIS
Extracellular potentials are generated by the current source-density, i. e., membrane currents that flow out or into the intracellular medium. The currents that flows through the membrane toward the extracellular medium (outward current) is called source. The current that flows through the membrane toward the intracellular space (inward current) is called sink.
Basic principles of current flow in the brain:
1. the currents are mainly resistive or ohmic, except through the cell membrane.
2. the currents flow in a closed loop.
In brain structures where the neurons are aligned parallel, like in the layered neocortex or hippocampus, with current source density analysis we can show the sites of synaptic action, and tell whether there happened a depolarization or hyperpolarization in the examined area. Examples for CSD map see Slides 48 and 49.
CURRENT SOURCE DENSITY (CSD) ANALYSIS
The current source density (CSD) is the sum of the transmembrane currents for all the neurons in a local volume. CSD is a descriptor for the current accumulation per volume of the extracellular medium, thus the term „density”.
In a local volume, different neurons may generate membrane currents of various magnitudes or polarities. Cancellation of positive and negative membrane currents may occur in the CSD. This underscores the fact that CSD is a macroscopic (field) rather than a microscopic (single neuronal) descriptor.
Volume conductor effects are eliminated, CSD describes the local macroscopic membrane currents.
A CSD map can be constructed from local field potential recorded with a multielectrode, which has sufficient contacts (min. 10 contacts, but around 24 are optimal). The contacts are evenly spaced (with for example 100 μm intercontact distance) in a linear fashion and the electrode is inserted paralell with the neurons in the
CURRENT SOURCE DENSITY (CSD) ANALYSIS
The CSD can be calculated as the second spatial derivative of the local field potentials.
In the case of the recordings with multielectrodes we can get the CSD in the following manner:
The CSD at electrode contact j is:
CSDj= -(ij-ij+1)/h
where ij is the estimated current and h is the intercontact distance.
ij=(uj-uj-1)rh
where uj is the field potential at contact j and r is the tissue resistance.
So the Three point formula is:
CSD(j)= -[u(j-1)-2u(j)+u(j+1)]/rh2 And the Five point formula:
CSD(j)= -[2u(j-2) -u(j-1) -2u(j)+u(j+1) +2u(j+2) ]/rh2
CSD of the averaged auditory evoked potentials recorded with a 23 contact multielectrode from the auditory cortex of the cat during slow-wave sleep. Sinks are indicated with red
CSD
Alternating patterns of sinks (blue) and sources (red) in the rat somatosensory cortex during ketamine-xylasine anesthesia.
REFERENCES, FURTHER READING
• J. A. Stamford (ed.), Monitoring Neuronal Activity, Oxford University Press, 1992
• P. Michael Conn (ed.), Electrophysiology and Microinjection, Academic Press, 1991
• F. Bretschneider, J. R. de Weille, Introduction to Electrophysiological Methods and Instrumentation, Elsevier, 2006
• E. R. Kandel, J. Schwartz, T. Jessell (eds.), Principles of Neural Science, 4th ed., Elsevier, 2000
• U. Mitzdorf, Current Source-Density Method and Application in Cat Cerebral Cortex: Investigation of Evoked Potentials and EEG Phenomena
,
Physiological Reviews, Vol. 65, No. 1. (January 1985), pp. 37-100.• G. Buzsáki, Large-scale recording of neuronal ensembles, Nature neuroscience, Vol. 7, No. 5. (May 2004), pp. 446-451
REVIEW QUESTIONS
• On which factors depend the recorded brain bioelectric signal parameters?
• How many neurons and synapses can be found in 1 mm3 of cortical tissue?
• What is the difference between action and postsynaptic potentials?
• In which direction flow the ions at an excitatory postsynaptic potential?
• In which direction flow the ions at an inhibitory postsynaptic potential?
• What are the three types of neuronal population induced potential fields?
• What is an equivalent dipole? What orientations can it have?
• What is standard 10-20 EEG electrode system?
• Why is potential source localization an inverse and ill-posed problem?
• What are the different types of solutions for this problem?
• What is the three-shell spherical head model? Why is it necessary?
• List and characterize three different source localization methods!
• What is current source density analysis? Why is it useful? What are the limits of this method?
