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From Neuronal activity to EEG/MEG signals

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1 From Neuronal activity to EEG/MEG signals
A short tale about the origins of Electroencephalography and Magnetoencephalography There might not be complete beginners in the room, I suspect you all know at least a little about EEG & MEG. So this introductary lecture is more like a reminder about what we measure with EEG and MEG. It is meant to put you in the mood for electrophysiology in humans for the coming three days and to motivate the methods you’ll learn about all along the theoretical and practical sessions. Jérémie Mattout U821 INSERM Brain Dynamics and Cognition Lyon, France SPM Course – May 2010 – London

2 The EEG & MEG instrumentation What do we measure with EEG & MEG ?
Outline A brief history The EEG & MEG instrumentation What do we measure with EEG & MEG ? Of the importance of modelling forward Here is the outline of the talk I will start with a brief history of EEG & MEG as recording techniques We will then focus on the instrumentation without getting into to much details but just a get the broad picture of the measurement principles and to emphasize the type of activity that we obtain on scalp. This will be the main part of the talk. Finally, having in mind the general principles of EEG & MEG signal generation, we will stress the importance of modelling and define forward modelling of EEG/MEG data which will be the explicit ground for most of the inference methods you’ll hear about in the other talks.


4 Carl Friedrich Gauss Lionel Messi

5 A brief history

6 A brief history From the electrical nature of brain signals …
1875: R.C. measured currents inbetween the cortical surface and the skull, in dogs and monkeys Richard Caton … to the first EEG recordings Of couse we could travel very far back in time to trace the origins of EEG and MEG. A reasonable starting point is the end of the 19th century, with the work of a british physician, Richard Caton, who was the first to measure brain electrical currents in animals. He had the top of their head choped and could thus put an electrode on top of the brain and another reference electrode on the skull. And then by connecting a galvanometer (the ancester of the Ampere-meter) he could measure tiny current flows. At that time already, he already described differences in those currents, for instance between sleep and awake states, he also demonstrated that those currents were indeed coming from a living brain since after death, those currents would slowly dissapear. Later on, about 50 years later, Hans Berger, a german neurologist got interested in understanding the mind and is credited for having invented the word EEG. Indeed he was one of first to record and describe variations in scalp electric potentials in humans and described signals such as alpha and beta waves This was more or less the birth of brain electrophysiology, especially in humans and the birth of EEG. 1924: H.B. first EEG in humans, description of alpha and beta waves Hans Berger Alpha actiity ~ 200 μV

7 A brief history About 50 years later … 1962: Josephson effect
1968: first (noisy) measure of a magnetic brain signal [Cohen, Science 68] 1970: James Zimmerman invents the ‘Superconducting quantum interference device’ (SQUID) 1972: first (1 sensor) MEG recording based on SQUID [Cohen, Science 1972] 1973: Josephson wins the Nobel Prize in Physics Brian-David Josephson But as you know MEG is much younger. One had to wait for another 50 years and a little revolution in physics to be able to record the first MEG signal. Indeed, in 1962, during his PhD, the british physicist Brian-David Josephson described the ‘Josephson effect’ (a special case of tunnel effect) which enables some conduction between two superconducting materials seperated by a thin layer of an insulating material, even in the absence of any external voltage. This property is exploited in the so-called Josephson junction whose one of the main application is the SQUID. And the SQUID proved of particular interest to build very sensitive magnetometers. - The SQUID itself was invented by J. Zimmerman, a north american researcher working for the Ford Compagny. - Thanks to the SQUID, David Cohen, at the MIT, significantly improved his MEG device and published the first modern MEG recordings in 1972, one year before the 30 years old Josephson was awarded the Nobel Prize in Physics. David Cohen

8 A brief history About 40 years later… today! Bob - 2010
- And this is how MEG systems look like today. They are made of about 300 sensors covering the whole head. They still involve the SQUID technology. AS it incorporates superconducting materials, it needs to be cooled down to 4°Kelvin (-269° Celsius). This is why there is a large container above the helmet. It contains liquid helium. What is also required so far is the shielded room that prevent the very sensitive sensors from recording noisy signals (we’ll come back to that in a minute). Those shielded rooms can be single-layered or double-layered, passive or active. Active means that they try to compensate, online, for field inhomogeneities. Shielded rooms are made of mu-metal (nickel, iron but also copper and molybden) against static magnetic fields (low frequencies) but also aluminium against high-frequencies. You might be aware that there are ongoing researches in physics to invent new MEG sensors and build new systems that would work at high temperature but this is future… Regarding EEG, systems are also evolving, not only to enable simultaneous recordings with fMRI but as here wireless system did appear recently and some of them even clame to be dry, meaning that you don’t even need to add conducting gel, to be tested… Bob

9 The EEG & MEG instrumentation

10 The EEG & MEG instrumentation
Claire & JB (french scientists) The EEG cap sticks to the subject’s head EEG measures are not much sensitive to environmental noise (except for 50Hz) EEG data depend upon a choice of reference EEG data might be corrupted by artefacts (blinks, saccades, heart beat, sweat, muscle activity, breathing, swallowing, yawning, sweat, 50Hz, ) There is not much to say about EEG. Current systems use a soft cap whose size is adapted to the subject’s head. It is always a compromise between confort and good contact. The technology is simple and known for long, we simply measure differences in electric potential on the scalp. Those differences are of the order of hundreds of micro-volts. Two important aspects that differ from MEG: - the sensors lie on the subject’s head surface, meaning that electrodes rarely move with respect to the subject, this is convinient for precise co-registration with the anatomy. - Since we measure potential differences, the observations depend on how we choose the reference electrode. This is something we need to keep in mind when we interpret the data and want to model the spatial topographies of scalp potentials.

11 The EEG & MEG instrumentation
- 269 °C SQUIDs Now, the MEG is a little more complex and it is useful to have a quick look inside. Here is the real aspect of the MEG recording system and here is a schematic of the inside of the Dewar. So contrary to EEG, the sensors have fixed position and this the subject’s head location that is fit to the helmet. Inside, the dewar is full of liquid helium and is thermically isolated from the outside thanks to vacuum space all around it. Sensors (Pick up coil)

12 The EEG & MEG instrumentation
There are different types of sensors Magnetometers: measure the magnetic flux through a single coil Gradiometers: measure the difference in magnetic flux between two points in space (axial/planar ; order 1, 2 or 3) There are different types of MEG sensors. In all cases, they use coils that transform the magnetic flux through the surface coil into a tiny electric current whose intensity will be instantaneously compensated and hence measured by the SQUID. This is the amount of compensatory current that is related to the magnetic field and yield the MEG signal. Now with a single coil, we get a magnetometer that measures the local magnetic field directly. Other systems like the one downstairs from CTF is using gradiometers. Here is a 1st order axial gradiometer. Axial because the z vertical axis is radially oriented with respect to the scalp. 1st order because it is made of two coils and thus computes the first derivative of the magnetic flux locally by computing the difference between the two opposite currents generated in each coil. One can even couple gradiometers to compute higher order differences and planar instead of axial gradiometers also exist. Gradiometers are less sensitive to distant sources, meaning that they are both less sensitive to noise from the environment and to deep sources. This is why some MEG systems like the finish Elekta machine do couple magnetometers and gradiometers. The type of sensors depend upon the machine you have. However, there are some mathematical tranformations that enable you to represent your data in one way or another, a bit like Laplacian operators transform the EEG data into maps of SCD.

13 The EEG & MEG instrumentation
MEG essentially measures… noise! Heart beat Eye movements Brain activity Evoked brain activity Biomagnetic fields Earth magnetic field Environmental noise Urban noise Car (50m) Screw driver (5m) Electronic circuit (2m) 1 femto-Tesla (fT) = T Alpha waves ~ 103 fT Although this is a beautiful technology, what we essentially measure with MEG is noise. Indeed, brain activity generates magnetic fields of the order of a hundred to a thousand fT where Tesla is the common unit for magnetic fields and fT indicates a magnitude of T; in other words brain magnetic fields are a billion time smaller than the earth magnetic field. Here are other examples with order of magnitudes: a car passing by 50 meters away creates a magnetic field that is a thousand times higher than the one generated by brain activity. This explains the need for a shielded room and it is a bad idea to enter the MEG room with metal on you. However, nowadays, MEG can be installed in city centers, not far away from MR scanners and it works!

14 What do we measure with EEG & MEG ?
from a single neuron to a neuronal assembly

15 What do we measure with EEG & MEG ?
From a single neuron to a neuronal assembly/column A single active neuron is not sufficient. ~ simultaneously active neurons are needed to generate scalp measures. Pyramidal cells are the main direct neuronal sources of EEG & MEG signals. Synaptic currents but not action potentials generate EEG/MEG signals What are the current sources within the brain that we measure with EEG & MEG ? Given our current knowledge of human brain physiology, signals of interest come from the synchronous activity of groups of neurons that are closed to each other and exhibit a similar pattern of activity. Indeed, a single neuron alone won’t be able to elicit a measurable signal on scalp but a whole population of several thousands who activate synchronously can. In fact, among cortical neurons, pyramidal cells are believed to be the main sources of the EEG and MEG signals. This is because they are roughly parallel to each other and oriented perpendicular to the cortical surface so that when they activate simultaneously, their contributions sum up into a macroscopic current. Finally, these currents reflect synaptic current mostly and not action potentials. This is because action potentials generate currents in both opposite directions along the axons so that the sum of their effects is closed to zero.

16 What do we measure with EEG & MEG ?
The dipolar model source sink An active neuronal column is thus represented by a parametric model, a dipolar source, whose parameters are the dipole position, its orientation and its intensity, hence 6 parameters. Another feature of the source currents is that, given the size of the head, they happen to be fast enough to consider that there is no propagation delay, from the neurons to the sensors. In other words, the effect of neuronal activity is immedialty reflected on the scalp. This has the important consequence of greatly simplifying the equations one has to solve in order to model how brain sources express on the EEG or MEG sensors. We’ll come back to that in a minute. A current source in the brain corresponds to a neuronal column and is modelled by a current dipole A current dipole is fully defined by 6 parameters: 3 for its position & 3 for its moment (includes orientation and amplitude) A dipolar moment Q = I x d ~ 10 to 100 nAm

17 What do we measure with EEG & MEG ?
from a neuronal assembly to sensors

18 What do we measure with EEG & MEG ?
From a single source to the sensor: the quasi-static assumption Let’s see now how such a macroscopic source modelled by a current dipole generates EEG and MEG signals repsectively. Starting with EEG, here is the example of a single source. We refer to the synaptic (intra-cellular) currents (the dipolar curent) as primary or source current, to be distinguished with their consequences in the extra-cellular media: the secondary or conduction currents. E: electric field B: magnetic field James Clerk Maxwell ( )

19 secondary/conduction
What do we measure with EEG & MEG ? From a single source to the sensor: EEG Electric field lines Let’s see now how such a macroscopic source modelled by a current dipole generates EEG and MEG signals repsectively. Starting with EEG, here is the example of a single source. We refer to the synaptic (intra-cellular) currents (the dipolar curent) as primary or source current, to be distinguished with their consequences in the extra-cellular media: the secondary or conduction currents. primary/source currents secondary/conduction currents Js Jc

20 What do we measure with EEG & MEG ?
From a single source to the sensor: EEG Ohm’s law Jc = s E = - s grad(V) s : tissue conductivities Georg Simon Ohm Indeed, currents need to flow to complete their loop from the source to the sink. In doing so, they obey two important laws: One is Ohm’s law which relates the source current to the electric field and hence to the potentials we measure with EEG on the scalp. The second is the conservation law which relates the primary and secondary currents and hence the source current to the potential itself. Importantly, this emphasizes the dependency upon the tissue conductivities. This explains why EEG is sensitive to inhomogeneities in conductance and why it might be important when modelling EEG data to account for those inhomogeneities in each of the head tissue. Margaret Thatcher Queen Elisabeth II Conservation law .Js + . Jc = 0 => . Js = .[s grad(V)]

21 What do we measure with EEG & MEG ?
From a single source to the sensor: EEG Simulated example Early auditory evoked repsonse Here is an example of the electric potential elicited on scalp by a single dipole (here in white). Whatever the dipole orientation, one observe potential differences on scalp. However, depending on the orientation, one might see two patterns (one positive and one negative) or only one of the two pattern. Moreover, as you can see on this example, the patterns are very smooth, the dipole activity affects almost all sensors. This means that when several sources are active, what we get on the scalp is a blurred image of the activity underneath which is difficult to disentangle and interpret. To better understand the cause of this blurring, here is a simulation of a single source activity What is represented here is the potential on each surface of the different tissues. - This is after conduction through the brain, up to the inner skull surface. The potential distribution is quite focal. This is now on up to the outer skull surface. The image is much smoother and ressembles very much the one we finally get on scalp. This highlights the blurring effect due to the skull. The skull is indeed very inhomogeneous (its width varies from place to place, there are cavities and moreover, it is highly anisotropic in the sense that conductivities depend upon the direction of the current flow. - As a consequence, to properly model EEG data, one has to account for the sensitivity of the bioelectric potential to those anatomical and physical factors. We’ll come to that in a minute. EEG is sensitive to both radial and tangential sources EEG is sensitive to conductivities which explains the low resolution scalp topographies To model EEG data, it matters to account for real tissue conductivity and geometry

22 What do we measure with EEG & MEG ?
From a single source to the sensor: MEG > Right hand rule Let’s now consider, as we just did with EEG, how a single source generates MEG signal. Given a source in the brain, its location and moment, the direction of the magnetic field lines is given by the (very well known) right hand rule. In this example, applying the right hand rule, one observe that a tangential source (that is parallel to the scalp surface and hence to the coil) yield to lines (here in blue) that flow through the coil. At the contrarery, radial sources such as the green one on the figure, generate lines that do not flow through the coil. This raises two questions: does MEG have a different sensitivity to tangential sources compare to radial sources, in contradistinction with EEG ? How this gradiometer which, I remind you, measures the difference in the magnetic field amplitude along the z-axis between the two coils… how does this difference can inform us about the source ? Barak Obama

23 What do we measure with EEG & MEG ?
From a single source to the sensor: MEG Well, to answer the first question, indeed MEG is much more sensitive to tangential sources than to radial ones. However, to be fair with MEG, it is quite unlikely, given the non-spherical shape of the head and the folded nature of the cortex that a source would be strictly radial with respect to all sensors. As you can see on this toy example, MEG is not completely blind to a radial source… This map gives me the opportunity to emphasize that what is represented here is the amplitude of the magnetic field on the radial axis. In fact, the difference in magnetic flux in the case of gradiometers as here. Also importantly, you notice that this topography is much less blurred than for EEG. The color code is not that important here. What is important is how to interpret this map. And for 1st gradiometers it is quite convenient since a bipolar pattern like this is a strong indication in favor of a single dipole lying inbetween the two poles. Radial dipole Tangential dipole

24 What do we measure with EEG & MEG ?
Biot & Savart’s law From a single source to the sensor: MEG source orientation & size source amplitude Félix Savart ( ) Jean-Baptiste Biot ( ) The Biot & Savart Law gives the magnetic field intensity generated by a dipolar source of size dl, at position r’ and intensity I at a sensor location r. What’s important to note is that the magnetic field, its intensity or norm since we are dealing with vector quantities here, is proportional to the inverse of the square of the distance between the source and the sensor. As a consequence: MEG is indeed less sensitive to deep sources but also, this law clarifies how MEG works. If one knows the distance between the two coils of a single gradiometer, the difference in magnetic field between the two coils will inform us about the dipole intensity, location and orientation (provided you have several sensors). Finally, you notice that the magnetic field does not depend upon tissue conductivities, contrary to EEG. The magnetic equivalent is the permeability. However, all head tissues are amagnetic and their permeability is well approximated by the vacuum permeability mu0. source location sensor location The magnetic field amplitude decreases with the square of the distance between the source and the sensor => MEG is less sensitive to deep sources Pure radial sources will remain silent

25 What do we measure with EEG & MEG ?
From a single source to the sensor: MEG MEG EEG This implies that in contradistinction with electric potentials, magnetic fields won’t be distorted. This explains the more focal MEG topographies and why MEG is said to have a higher spatial resolution or equivalently a higher power of localisation. Here is the same example as earlier when we now can compare MEG and EEG for the same single dipole activity. As you can see, the dipolar pattenr on scalp is much more focal for MEG and as the magnetic field line are perpendicular to the electric field line, the EEG and MEG pattern are orthogonal to each other. This also emphasizes the complementarity of EEG and MEG which can easily be combined in the same experiment. --- Voici l’exemple d’une réponse évoquée à un stimulus auditif répété et la cartographie que l’on peut représenter en moyennant sur un grand nombre d’essais. A gauche l’EEG et à droite la MEG pour la même source dipolaire dans le cortex auditif primaire gauche. On observe dans les deux cas un pattern bipolaire. La source est superficiel et tangentielle, donc bien observable en MEG. En EEG, les pôles sont aux deux extrémités du dipoles tandis qu’en MEG, ils sont de part et d’autre. Le pattern MEG est beaucoup plus focal alors qu’il est très diffus en EEG. C’est parce que les milieux de la tête sont amagnétiques (cf. mu0), les lignes de champs sont très peu perturbées contrairement aux lignes de potentiel électrique! C’est ce qui procure une meilleure résolution spatiale à la MEG et qui en fait une modalité aux caractéristiques uniques.

26 What do we measure with EEG & MEG ?
Summary spatial resolution (mm) invasivity weak strong 5 10 15 20 temporal resolution (ms) 1 102 103 104 105 sEEG MEG EEG fMRI MRI(a,d) PET SPECT OI ECoG

27 Of the importance of modelling forward
« Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? » Jacques Hadamard ( )

28 Of the importance of modelling forward
From EEG/MEG data to neuronal sources ? inference MEG EEG

29 (conductivity & geometry)
Of the importance of modelling forward Forward model MEG Generative models EEG Head tissues (conductivity & geometry) Dipolar sources

30 Of the importance of modelling forward
Gain vectors & Lead-field matrix Simulating data Y = g() scalp data forward model source parameters 1 layer vs. 3 layers spheres vs. realistic surfaces or volumes analytical vs. numerical solutions 1 source 1 gain vector All sources 1 gain operator or lead-field matrix

31 Of the importance of modelling forward
Inverse problem Modelling empirical data Y = g(1) + g(2) +  scalp data forward Model (lead-fields) Unknown source Parameters ?

32 Karl Friston Will Penny Marta Garrido Stefan Kiebel Jean Daunizeau James Kilner Vladimir Litvak Guillaume Flandin Rik Henson Rosalyn Moran Christophe Phillips Gareth Barnes JM Schoffelen

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