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| = Tutorial 13: Head model = ''Authors: Francois Tadel, John C Mosher, Richard Leahy, Sylvain Baillet'' |
= Tutorial 20: Head modelling = ''Authors: Francois Tadel, Elizabeth Bock, John C Mosher, Richard Leahy, Sylvain Baillet'' |
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| This tutorial is still based on Sabine Meunier's somatotopy experiment, called ''TutorialCTF ''in your Brainstorm database. The recordings have already been imported and analyzed at the sensors level, they are ready for source estimation. | The following tutorials describe how brain activity can be estimated from the MEG/EEG recordings we have processed so far. This step consists in solving two separate modeling problems: the modeling of the electromagnetic properties of the head and of the sensor array (a.k.a. '''head model''' or '''forward model''') and the estimation of the brain sources which have produced the data. That second step is known as '''source modeling''' or solving an '''inverse problem'''. It requires that the forward modeling of the head tissues and sensor instrumentation is completed first. This tutorial explains how to compute a head model for the subject of the auditory oddball experiment.'' '' |
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| <<TableOfContents(2,2)>> | <<TableOfContents(2,2)>> '' '' |
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| == Why inverse models? == | <<TAG(Advanced)>> '' '' == Why estimating sources? == Reconstructing the activity of the brain from MEG or EEG recordings involves several sophisticated steps. Athough Brainstorm simplifies the procedures required, it is important to understand whether source modeling is essential to answer the neuroscience question which brought you to collect data in the first place. '' '' If one of your primary objectives is to '''identify and map''' the regions of the brain involved in a specific stimulus response or behaviour, source estimation can help address this aspect. Empirical interpretations of sensor topographies can inform where about brain generators might be located: which hemisphere, what broad aspect of the anatomy (e.g., frontal vs. posterior regions). Source estimation methods improves anatomical resolution with respect to the interpreration of sensor patterns. Spatial resolution in MEG and EEG depends on source depth and orientation and overall SNR: still, one can expect to be able to observe source activations within the millimeter to centimeter range, especially relatively, when contrasts between conditions are implemented in the study design. '' '' Source mapping is a form of '''spatial''' '''deconvolution''' of sensor data. In EEG in particular, scalp topographies are very smooth and it is common that contributions from distant brain regions overalp over large clusters of electrodes. Moving to the source space can help separating the active regions. '' '' More specifically in '''MEG''', source maps can be a great asset to alleviate some specific issues with that modality. In MEG, the head of the subject is not fixed. Hence sensor topographies depend on the actual position of the subject under the rigid helmet. Therefore, between two acquisition runs, or between subjects with different head shapes and sizes, '''the same''' '''MEG sensors may pick up signals from different parts of the brain'''. This problem does not exist in EEG, where electrode montages are attached to the head and arranged according to standard positions. '' '' Another important point to consider when interpreting MEG sensor maps is that MEG manufacturers use different types of sensor technology (e.g., magnetometers vs. gradiometers; axial vs. tangential gradiometers, etc. yielding different physical measures). This is not an issue with EEG, with essentially one sensor type (electrodes, dry or active, all measuring Volts): two EEG electrode caps with same number of electrodes only differ in how well they ensure good contact with the scalp. Working in source space alleviates all these aspects. '' '' Nevertheless, if your neuroscience question can be solved by measuring signal latencies over broad regions, or other aspects which do not depend crucially on anatomical localization (such as global signal properties integrated over all or clusters of sensors), source modeling might not be a requirement. To sort out this question will influence the time and hardware requirements to complete your data analysis (source analysis multiplies the needs in terms of disk storage and computational specifications). <<TAG(Advanced)>> '' '' == The origins of MEG/EEG signals == To better understand how the forward model is elaborated, we need to have at least a basic understanding of the physiological origins of MEG/EEG signals. Note that, as always when dealing with modeling, we need to deal with various degrees of approximation. '' '' Overall, it is assumed that most of the MEG/EEG signals are generated by postsynaptic activity of ensembles of cortical pyramidal neurons of the cerebral cortex. The reason is essentially in the morphology and mass effect of these cells, which present '''elongated shapes '''and are '''oriented''' '''perpendicularly to the cortical surface'''. Mass effects of close-to-simulatenous changes in post-synaptic potentials pyramidal neural assemblies add up in time and space. These effects can conveniently be modeled at a mesoscopic spatial scale with electric dipoles distributed along the cortical mantle (green arrows in figure below). Note that there is growing evidence that MEG and EEG are also sensitive to deeper, cortical and subcortical structures, including brain nuclei and the cerebellum, where pyramidal cells are rare or absent. Brainstorm features advanced models that can include as an option, these structures. The emphasis in the present tutorial is on pyramidal cell assemblies for simplicity. The primary and volume currents generated by these dipoles create differences in electrical potentials and magnetic fields that can be detected outside the head. They can be measured with electrodes placed on the skin (EEG, with respect to a reference) or very sensitive magnetic detectors (MEG). '' '' . {{attachment:origins.gif||height="342",width="538"}} '' '' . <<HTML(<div align="right"><FONT size="-1" color="#CCCCCC"><I>Matti Hamalainen, 2007</I></FONT></div>)>> '' '' <<TAG(Advanced)>> '' '' == Source space == '''Dipole fitting vs distributed models''' MEG/EEG source estimation consists in modeling brain activity with current dipoles. A current dipole is a convenient model equivalent to the net electrophysiological activity of local assemblies of neurons. Two main approaches have been explored for source MEG/EEG estimation: '''dipole fitting methods''' - where the position and amplitude of a one to a few equivalent current dipoles (ECD) are estimated over relativelyshort time windows - and '''distributed models''' - where the location (and typically, the orientation) of a large number dipoles is fixed. The dipoles sample a spatial grid covering the entire brain volume or the cortical surface - only their amplitude is estimated at each time point. '' '' Equivalent dipole fitting approaches are quite straightforward and can be adequate when the number of brain regions expected to be active is small. Therefore, it is most adequate for responses at early latencies. They cannot generalize to capture complex dynamics over extended period of time (epochs) and the associated estimation techniques are quite sensitive to intial conditions (how many dipoles to fit? Where does the serch start? etc.). Our strategy in Brainstorm is to promote distributed source models, which are less user-sensitive, can generalize to all experimental conditions, and yield time-resolved image volumes that can be processed in many different, powerful ways (group statistics, spatial segmentation, use of regions fo interest, correspondence with fMRI, etc.) '''Location constraints''' '' '' When opting for distributed source models, the '''positions and orientations of the elementary dipoles''' that will define the "voxel" grid of the source images produced need to be defined. This set of dipoles is called the '''source space'''. By default, Brainstorm constrains the source space to the '''cortex''', where signal-to-noise and sensitivity is maximum in MEG/EEG. Note however that more complete models that include subcortical structures and the cerebellum are available in Brainstorm. Therefore, one decision you need to make before proceeding with source imaging is whether more complete source spaces are required to answer your neuroscience question. For this tutorial, we use the simple approach where a current dipole is automatically assigned to each of the vertices of the cortical surface we have imported so far (see the nodes in the grey mesh in the leftmost image below). '' ''Also in this turorial, we elected not to contrain the dipole orientations to be perpendicular to the cortical surface. This choice can be motivated by the fact that you have no access to the individual MRI of your participant and thefore resort to a generic template, or that you find the cortical orientation constraint to be poorly unjustified. In this context, '''three orthogonal dipoles '''are assigned to each vertex of the cortex. This triplet forms a basis to account for local currents flowing in any arbitrary direction, not just orthogonal to the cortex. When importing the anatomy of the subject, we downsampled the cortex surface to '''15,000 vertices'''. This will correspond to a source space of '''45,000 dipoles'''. We will compute a forward model that connects the activity of these 45,000 dipoles with the 275 MEG sensors we have in this dataset. '' '' This default number of 15,000 vertices is empirical. Over the years, our experience seemed to show that it represents a good balance between the representation of the brain circumvolutions, the surface sampling and the amount of data that is generated. Using less vertices makes it difficult to preserve the shape of the brain, using more vertices produces more data without adding to the spatial resolution of the method and may lead to computational memory issues. '' '' '''Orientation constraints''' '' '' Additionally, we can impose '''constraints of orientation''' on the dipoles, to match the physiological observation that the pyramidal cells are mostly organized perpendicularly to the cortex surface. This has the advantage of limiting the number of dipoles to 15,000 (one per vertex) and making the results much easier to display and process. However, this constraint is most of the time too strong and distorts the reconstruction. This orientation constraint is an option of the inverse model and will be discussed in the following introduction tutorials. '' '' '''Fully unconstrained''' '' '' The spatial constraint of imposing all the dipoles to be on the cortical surface might also be too restrictive in some cases, because our model is then not able to correctly represent the activity in deeper brain structures or in the cerebellum. Therefore we also offer an option to use the '''entire brain volume''' as our source space (the green dots below represent dipoles locations in volume model). This produces results that can be better or worse depending on the data, but in all the cases much more difficult to review. Volume and mixed head volumes are discussed in the advanced tutorials about source modeling. '' '' . {{attachment:source_space.gif||height="200",width="243"}} {{attachment:source_volume.gif||height="200",width="255"}} '' '' <<TAG(Advanced)>> '' '' |
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| The first step consists in computing a model that explains how an electric current flowing in the brain can influence what is recorded out of the head, by the EEG or MEG sensors. | The first step of the source reconstruction consists in computing a model that explains how the electric currents or the magnetic fields flow from the electric generators in the brain (source space) through the different tissues of the head (mostly brain, CSF, skull and skin), to finally reach the sensors. '' '' |
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| * This problem is called forward problem. * Its result is called ''head model ''in Brainstorm interface, but can also be referred as ''forward model'' or ''leadfield matrix''. * In the Brainstorm software, we consider by default that the electric or magnetic activity which is recorded by the sensors is produced mainly by a set of electric dipoles located at the surface of the cortex.<<BR>> * The grid of sources (dipoles) that is used is defined by the cortex surface we have imported in one of the previous tutorials; each vertex of this surface is considered as a dipole. * The default surface distributed with Brainstorm have around 15,000 vertices. So we will have 15,000 dipole amplitudes to estimate. Using less vertices would just lower the resolution of the results; using more produces too much data and might lead to memory issues. * What we expect to get at the end of this process is a matrix whose size is [Number of sensors x Number of sources] * For computing this matrix, three methods are available for MEG recordings in Brainstorm: * '''Single sphere''': the head is considered a homogeneous sphere * '''Overlapping spheres''': Refining the previous model by fitting one local sphere for each sensor * '''OpenMEEG BEM''': Symmetric Boundary Element Method from the open-source software OpenMEEG. Described in an advanced tutorial: [[Tutorials/TutBem|BEM head model]]. |
* The question of building a model that connects the values we observe outside of the head (MEG/EEG) to the electric activity of the cortical dipoles in the brain is called '''forward problem'''. '' '' * The model we obtain after solving this problem is called '''head model''' in Brainstorm, but can also be referred to as '''forward model''', '''leadfield matrix''' or '''gain matrix'''. '' '' * In this tutorial we will use the default source space: the low-resolution cortex surface with 15,000 vertices, as the support of 45,000 dipoles. We will use indifferently the terms '''dipole''' and '''source'''. '' '' * What we expect to get at the end of this process is a matrix '''[Nsensors x Nsources]'''. <<BR>><<BR>> {{attachment:forward_inverse.gif}} '' '' |
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| {{attachment:forwardInverse.gif}} | ==== Available methods for MEG forward modeling ==== * '''Single sphere''': The head is considered as a homogeneous sphere. '' '' * '''Overlapping spheres''': Refines the previous model by fitting one local sphere for each sensor. '' '' * '''OpenMEEG BEM''': Symmetric Boundary Element Method from the open-source software OpenMEEG. Described in an advanced tutorial: [[Tutorials/TutBem|BEM head model]]. '' '' |
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| == Single sphere model == Select the ''TutorialCTF ''protocol, close all the figures, and follow these steps: |
==== Models recommended for each modality ==== * '''MEG''': Overlapping spheres.<<BR>>The magnetic fields are not affected too much by the heterogeneity of the tissues of the head. There is no real need for modeling the head with too much detail. '' '' * '''EEG''': OpenMEEG BEM.<<BR>>The electric currents are strongly affected by jumps between very conductive tissues (brain, CSF, skin) and an isolant medium (the skull). A realistic head model is advised for integrating the properties of the skull correctly. When computing a BEM model is not an option, for instance if OpenMEEG crashes for unknown reasons, the Berg's three-layer sphere can be an acceptable option. '' '' * '''sEEG/ECoG''': The OpenMEEG BEM option is the only one available. '' '' |
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| 1. Right-click on the ''Right'' condition and select ''Compute head model''. The ''Head modeler'' window will appear.<<BR>><<BR>> {{attachment:popupHeadModel.gif}} --- {{attachment:headModeler.gif}} 1. Set the options for your head model: * Source space: '''Cortex surface'''. <<BR>>The MRI volume option will be introduced in an advanced tutorial: [[Tutorials/TutVolSource|Volume source estimation]]. * Forward modeling method: '''Single sphere'''. * You can also edit the '''Comment '''field of the file that will be created (the string that will be representing the head model in the database explorer). * Click on ''Run''. |
== Computation == The forward models are related with the anatomy of the subject and the description of the sensors, therefore the menus associated to its computation are attached to the channel file. '' '' |
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| 1. Two other windows appear, to help you define the sphere. Estimating the best fitting sphere for a head is not always as easy as it looks like, because a human head is usually not spherical. <<BR>><<BR>> {{attachment:helpBfs.gif|editBfs.gif}} <<BR>><<BR>> {{attachment:editBfsFigure.gif}} * Read and follow the instructions in the help window. * Click on the ''Scalp ''button, move and resize the sphere manually, just to see how it works. * Click again on ''Scalp'': here we will use directly the estimation of the sphere based on the vertices of the ''Scalp ''surface (a simple least-squares fitting using all the vertices of the surface). * For EEG 3-shell spheres models, you just estimate and manipulate the largest sphere (scalp), and then use the ''Edit properties...'' button in the toolbar to define the relative radii of the 2 other spheres, and their respective conductivities. This will be described in another tutorial. * Click on ''Ok'', and wait for a few seconds. |
* In the imported '''Run#01''', right-click on the channel file or the folder > '''Compute head model'''. <<BR>>Keep the default options selected: Source space='''Cortex''', Forward model='''Overlapping spheres'''.<<BR>><<BR>> {{attachment:compute_popup.gif||height="161",width="254"}} {{attachment:compute_options.gif||height="247",width="211"}} '' '' * You obtain one new file in the database. It is always saved in the same folder as the channel file.<<BR>>There is not much you can do with this file except for using it for estimating sources. This will be the purpose of the following tutorials. '' '' * Right-click on the new head model > ''Check spheres''. This window shows the spheres that were estimated. You can check them by following the indications written in green at the bottom of the window: use left/right arrows. At each step, the current sensor marker is displayed in red, and the sphere you see is its local estimation of the inner skull shape. <<BR>><<BR>> {{attachment:headmodel_popup.gif||height="124",width="258"}} {{attachment:headmodel_spheres.gif||height="181",width="272"}} '' '' * This algorithm is supposed to use the inner skull surface from the subject, but we usually do not have this information. In this case, a pseudo-innerskull is reconstructed using a dilated version of the cortex envelope. '' '' |
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| 1. A new file appeared just below the channel file, it represents the head model.<<BR>><<BR>> {{attachment:headModelPopup.gif}} * There is not much you can do with this file, as it is only a matrix that converts the cortical sources into MEG/EEG recordings, and we do not have any sources information yet. * You may just check the sphere(s) that were used to compute the head model. |
Repeat the same operation for the other file. We have two different acquisition runs with two different relative position of the head and the sensors, therefore we need to compute two different head models. '' '' |
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| == Overlapping spheres model == Let's compute a more advanced forward model. The overlapping spheres method is based on the estimation of a different sphere for each sensor. Instead of using only one sphere for the whole head, it estimates a sphere that fits locally the shape of the head in the surroundings of each sensor. |
* In the imported '''Run#02''', right-click on the channel file > '''Compute head model'''. <<BR>><<BR>> {{attachment:run02_popup.gif||height="220",width="265"}} {{attachment:run02_files.gif||height="220",width="193"}} '' '' |
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| 1. Right-click on ''Right'' condition and select ''Compute head model'' again. 1. Select the ''Overlapping spheres'' method and click on ''Run''. 1. This algorithm is supposed to use the inner skull surface from the subject, but we usually do not have this information. In this case, a pseudo-innerskull is reconstructed using a dilated version of the cortex envelope. 1. Right-click on the new head model > ''Check spheres''. This window shows the spheres that were estimated. You can check them by following the indications written in green at the bottom of the window: use left/right arrows. At each step, the current sensor marker is displayed in red, and the sphere you see is its local estimation of the head shape. 1. Close this window when you reviewed them all.<<BR>><<BR>> {{attachment:osTree.gif}} {{attachment:checkSpheres.gif}} 1. Compute a head model for the Left condition (Overlapping spheres). |
<<TAG(Advanced)>> '' '' |
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| == Selection of a head model == We now have two head models in for our ''Subject01 / Right'' condition. |
== Database explorer == Additional considerations about the management of the head model files. '' '' |
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| * You can have several head models computed for the same dataset, but it is not recommended as it might be difficult afterwards to know which one was used to compute the sources. * If you want to keep them anyway, you have to indicate which one is the default one. You do that by double-clicking on one of them (or right-click > set as default head model), and it is supposed to turn green. The head model displayed in green is the one that will be used for the following computation steps. * For MEG, when it works properly, the overlapping spheres model usually gives better results than the single sphere one. In this particular case, it produces more focal results, so we are going to use it for the next steps. * For EEG, always prefer the "OpenMEEG BEM" model. * Now to make things clearer: delete the'' Single sphere'' head model, and keep the ''Overlapping spheres''. |
* If you have '''multiple head models''' computed in the same folder, you would see one displayed in green and the others in black. The one in green is selected as the default head model, it will be used for all the following computation steps. To change the default selection, double-click on another head model file (or right-click > Set as default head model). '' '' |
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| == Batching head model computation == You can run in two clicks the computation of the overlapping spheres model for all the conditions or subjects you want in the database. |
* You can use the database explore for '''batching the computation''' of the head model. The menu "Compute head model" is available in popup menus in the database explorer at all the levels. It is applied recursively to all the folders contained in the node(s) you selected. '' '' |
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| * The ''Compute head model'' menu is available in popup menus in the tree at all the levels (protocol, subject, condition). It is then applied recursively to all the subjects and conditions contained in the node(s) you selected. * Example: If you want to compute it on all the subjects and all the conditions, select the ''Compute head model'' menu from the protocol node ''TutorialCtf''. For all the conditions of ''Subject01'', run it from the ''Subject01 ''popup menu. Etc. * If you only want to compute it on some subjects of the protocol, select them at once holding the ''Ctrl ''key, right-click on one, and select the ''Compute head model ''menu''.'' * To process all the subjects for one condition, switch to the ''Functional data (sorted by conditions)'' view of the database. |
<<TAG(Advanced)>> '' '' |
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| == Additional discussions on the forum == * Sensor modeling: http://neuroimage.usc.edu/forums/showthread.php?1295 * Gain matrix: http://neuroimage.usc.edu/forums/showthread.php?918 * EEG reference: http://neuroimage.usc.edu/forums/showthread.php?1525#post6718 * EEG and default anatomy: http://neuroimage.usc.edu/forums/showthread.php?1774 * Mixed head models indices: http://neuroimage.usc.edu/forums/showthread.php?1878 |
== On the hard drive == Right-click on any head model > File > View file contents: '' '' |
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| = From continuous tutorials: = == Source analysis == Let's reproduce the same observations at the source level. The concepts related with the source estimation are not discussed here; for more information, refer to the introduction tutorials #6 to #8. |
. {{attachment:headmodel_contents.gif||height="440",width="486"}} '' '' |
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| First, '''delete''' all the files related with the source estimation calculated in the previous tutorials, available in the ''(Common files)'' folder: the head model, the noise covariance and inverse model. We can now provide a better estimate of the noise (affects the inverse model), and we defined new SSP operators (affects the head model). | ==== Structure of the head model files: headmodel_*.mat ==== * '''MEGMethod''': Forward model used for MEG sensors ('os_meg', 'meg_sphere', 'openmeeg' or empty). '' '' * '''EEGMethod''': Forward model used for EEG sensors ('eeg_3sphereberg', 'openmeeg' or empty). '' '' * '''ECOGMethod''': Forward model used for ECoG sensors ('openmeeg' or empty). '' '' * '''SEEGMethod''': Forward model used for sEEG sensors ('openmeeg' or empty). '' '' * '''Gain''': Leadfield matrix, [Nsensors x Nsources], equivalent to [Nsensors x 3*Nvertices] '' '' * '''Comment''': String displayed in the database explorer to represent this file. '' '' * '''HeadModelType''': Type of source space used for this head model ('surface', 'volume', 'mixed'). '' '' * '''GridLoc''': [Nvertices x 3], (x,y,z) positions of the grid of source points. In the case of a surface head model, it corresponds to a copy of the 'Vertices' matrix from the cortex surface file. '' '' * '''GridOrient''': [Nvertices x 3], direction of the normal to the surface for each vertex point (copy of the 'VertNormals' matrix of the cortex surface). Empty in the case of a volume head model. '' '' * '''GridAtlas''': In the case of mixed head models, contains a copy of the "Source model options" atlas structure that was used for creating the model. '' '' * '''SurfaceFile''': Relative path to the cortex surface file related with this head model. '' '' * '''Param''': Description of the sphere that was estimated for each sensor (Center/Radius).<<BR>> '' '' |
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| === Head model === Right-click on any node that contains the channel file (including the channel file itself), and select: "'''Compute head model'''". Leave all the default options: cortex source space, and overlapping spheres. The lead field matrix is saved in file "Overlapping spheres" in ''(Common files)''. |
'''Gain matrix''' '' '' |
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| {{http://neuroimage.usc.edu/brainstorm/Tutorials/TutRawAvg?action=AttachFile&do=get&target=forward.gif|forward.gif|class="attachment"}} | * The Gain matrix stores the leadfield for 3 orientations (x,y,z) at each grid point (p1, p2, ...). <<BR>>The successive columns of the Gain matrix are: ['''p1'''_x, '''p1'''_y, '''p1'''_z, p2_x, p2_y, p2_z ...] '' '' * To convert this unconstrained leadfield matrix to a '''constrained model''', where the orientation of each dipole is fixed and normal to the cortex surface: '' '' * Export the head model file to the HeadModel structure: Right-click > File > '''Export to Matlab'''. '' '' * > Gain_constrained = '''bst_gain_orient'''(HeadModel.Gain, HeadModel.GridOrient); '' '' * The dimension of the output matrix is three times smaller: [Nsensors x Nvertices] '' '' |
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| = From auditory = === Head model === * Select the two imported folders at once, right-click > Compute head model . {{http://neuroimage.usc.edu/brainstorm/Tutorials/Auditory?action=AttachFile&do=get&target=headmodel1.gif|headmodel1.gif|height="221",width="413",class="attachment"}} * Use the '''overlapping spheres''' model and keep all of the options at their default values. . {{http://neuroimage.usc.edu/brainstorm/Tutorials/Auditory?action=AttachFile&do=get&target=headmodel2.gif|headmodel2.gif|height="234",width="209",class="attachment"}} {{http://neuroimage.usc.edu/brainstorm/Tutorials/Auditory?action=AttachFile&do=get&target=headmodel3.gif|headmodel3.gif|height="208",width="244",class="attachment"}} * For more information: [[http://neuroimage.usc.edu/brainstorm/Tutorials/TutHeadModel|Head model tutorial]]. |
== References == * Huang MX, Mosher JC, Leahy RM (1999)<<BR>>"A sensor-weighted overlapping-sphere head model and exhaustive head model comparison for MEG," Phys Med Biol, 44:423-440 | [[http://neuroimage.usc.edu/paperspdf/PMB99.pdf|pdf]] '' '' |
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| == On the heard drive == how to get the constrained leadfield |
== Additional documentation == * Tutorial: [[Tutorials/TutBem|BEM with OpenMEEG]] '' '' * Tutorial: [[Tutorials/TutVolSource|Volume source estimation]] '' '' * External documentation: [[http://www.canada-meg-consortium.org/EN/MegBaillet5|Electromagnetic neural source imaging]] * Forum: Sensor modeling: http://neuroimage.usc.edu/forums/showthread.php?1295 '' '' * Forum: EEG reference: http://neuroimage.usc.edu/forums/showthread.php?1525#post6718 '' '' * Forum: EEG and default anatomy: http://neuroimage.usc.edu/forums/showthread.php?1774 '' '' * Forum: Mixed head models indices: http://neuroimage.usc.edu/forums/showthread.php?1878 '' '' |
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Tutorial 20: Head modelling
Authors: Francois Tadel, Elizabeth Bock, John C Mosher, Richard Leahy, Sylvain Baillet
The following tutorials describe how brain activity can be estimated from the MEG/EEG recordings we have processed so far. This step consists in solving two separate modeling problems: the modeling of the electromagnetic properties of the head and of the sensor array (a.k.a. head model or forward model) and the estimation of the brain sources which have produced the data. That second step is known as source modeling or solving an inverse problem. It requires that the forward modeling of the head tissues and sensor instrumentation is completed first. This tutorial explains how to compute a head model for the subject of the auditory oddball experiment.
Contents
Why estimating sources?
Reconstructing the activity of the brain from MEG or EEG recordings involves several sophisticated steps. Athough Brainstorm simplifies the procedures required, it is important to understand whether source modeling is essential to answer the neuroscience question which brought you to collect data in the first place.
If one of your primary objectives is to identify and map the regions of the brain involved in a specific stimulus response or behaviour, source estimation can help address this aspect. Empirical interpretations of sensor topographies can inform where about brain generators might be located: which hemisphere, what broad aspect of the anatomy (e.g., frontal vs. posterior regions). Source estimation methods improves anatomical resolution with respect to the interpreration of sensor patterns. Spatial resolution in MEG and EEG depends on source depth and orientation and overall SNR: still, one can expect to be able to observe source activations within the millimeter to centimeter range, especially relatively, when contrasts between conditions are implemented in the study design.
Source mapping is a form of spatial deconvolution of sensor data. In EEG in particular, scalp topographies are very smooth and it is common that contributions from distant brain regions overalp over large clusters of electrodes. Moving to the source space can help separating the active regions.
More specifically in MEG, source maps can be a great asset to alleviate some specific issues with that modality. In MEG, the head of the subject is not fixed. Hence sensor topographies depend on the actual position of the subject under the rigid helmet. Therefore, between two acquisition runs, or between subjects with different head shapes and sizes, the same MEG sensors may pick up signals from different parts of the brain. This problem does not exist in EEG, where electrode montages are attached to the head and arranged according to standard positions.
Another important point to consider when interpreting MEG sensor maps is that MEG manufacturers use different types of sensor technology (e.g., magnetometers vs. gradiometers; axial vs. tangential gradiometers, etc. yielding different physical measures). This is not an issue with EEG, with essentially one sensor type (electrodes, dry or active, all measuring Volts): two EEG electrode caps with same number of electrodes only differ in how well they ensure good contact with the scalp. Working in source space alleviates all these aspects.
Nevertheless, if your neuroscience question can be solved by measuring signal latencies over broad regions, or other aspects which do not depend crucially on anatomical localization (such as global signal properties integrated over all or clusters of sensors), source modeling might not be a requirement. To sort out this question will influence the time and hardware requirements to complete your data analysis (source analysis multiplies the needs in terms of disk storage and computational specifications).
The origins of MEG/EEG signals
To better understand how the forward model is elaborated, we need to have at least a basic understanding of the physiological origins of MEG/EEG signals. Note that, as always when dealing with modeling, we need to deal with various degrees of approximation.
Overall, it is assumed that most of the MEG/EEG signals are generated by postsynaptic activity of ensembles of cortical pyramidal neurons of the cerebral cortex. The reason is essentially in the morphology and mass effect of these cells, which present elongated shapes and are oriented perpendicularly to the cortical surface. Mass effects of close-to-simulatenous changes in post-synaptic potentials pyramidal neural assemblies add up in time and space. These effects can conveniently be modeled at a mesoscopic spatial scale with electric dipoles distributed along the cortical mantle (green arrows in figure below). Note that there is growing evidence that MEG and EEG are also sensitive to deeper, cortical and subcortical structures, including brain nuclei and the cerebellum, where pyramidal cells are rare or absent. Brainstorm features advanced models that can include as an option, these structures. The emphasis in the present tutorial is on pyramidal cell assemblies for simplicity.
The primary and volume currents generated by these dipoles create differences in electrical potentials and magnetic fields that can be detected outside the head. They can be measured with electrodes placed on the skin (EEG, with respect to a reference) or very sensitive magnetic detectors (MEG).
- Matti Hamalainen, 2007
Source space
Dipole fitting vs distributed models
MEG/EEG source estimation consists in modeling brain activity with current dipoles. A current dipole is a convenient model equivalent to the net electrophysiological activity of local assemblies of neurons. Two main approaches have been explored for source MEG/EEG estimation: dipole fitting methods - where the position and amplitude of a one to a few equivalent current dipoles (ECD) are estimated over relativelyshort time windows - and distributed models - where the location (and typically, the orientation) of a large number dipoles is fixed. The dipoles sample a spatial grid covering the entire brain volume or the cortical surface - only their amplitude is estimated at each time point.
Equivalent dipole fitting approaches are quite straightforward and can be adequate when the number of brain regions expected to be active is small. Therefore, it is most adequate for responses at early latencies. They cannot generalize to capture complex dynamics over extended period of time (epochs) and the associated estimation techniques are quite sensitive to intial conditions (how many dipoles to fit? Where does the serch start? etc.). Our strategy in Brainstorm is to promote distributed source models, which are less user-sensitive, can generalize to all experimental conditions, and yield time-resolved image volumes that can be processed in many different, powerful ways (group statistics, spatial segmentation, use of regions fo interest, correspondence with fMRI, etc.)
Location constraints
When opting for distributed source models, the positions and orientations of the elementary dipoles that will define the "voxel" grid of the source images produced need to be defined. This set of dipoles is called the source space. By default, Brainstorm constrains the source space to the cortex, where signal-to-noise and sensitivity is maximum in MEG/EEG. Note however that more complete models that include subcortical structures and the cerebellum are available in Brainstorm. Therefore, one decision you need to make before proceeding with source imaging is whether more complete source spaces are required to answer your neuroscience question.
For this tutorial, we use the simple approach where a current dipole is automatically assigned to each of the vertices of the cortical surface we have imported so far (see the nodes in the grey mesh in the leftmost image below). Also in this turorial, we elected not to contrain the dipole orientations to be perpendicular to the cortical surface. This choice can be motivated by the fact that you have no access to the individual MRI of your participant and thefore resort to a generic template, or that you find the cortical orientation constraint to be poorly unjustified.
In this context, three orthogonal dipoles are assigned to each vertex of the cortex. This triplet forms a basis to account for local currents flowing in any arbitrary direction, not just orthogonal to the cortex.
When importing the anatomy of the subject, we downsampled the cortex surface to 15,000 vertices. This will correspond to a source space of 45,000 dipoles. We will compute a forward model that connects the activity of these 45,000 dipoles with the 275 MEG sensors we have in this dataset.
This default number of 15,000 vertices is empirical. Over the years, our experience seemed to show that it represents a good balance between the representation of the brain circumvolutions, the surface sampling and the amount of data that is generated. Using less vertices makes it difficult to preserve the shape of the brain, using more vertices produces more data without adding to the spatial resolution of the method and may lead to computational memory issues.
Orientation constraints
Additionally, we can impose constraints of orientation on the dipoles, to match the physiological observation that the pyramidal cells are mostly organized perpendicularly to the cortex surface. This has the advantage of limiting the number of dipoles to 15,000 (one per vertex) and making the results much easier to display and process. However, this constraint is most of the time too strong and distorts the reconstruction. This orientation constraint is an option of the inverse model and will be discussed in the following introduction tutorials.
Fully unconstrained
The spatial constraint of imposing all the dipoles to be on the cortical surface might also be too restrictive in some cases, because our model is then not able to correctly represent the activity in deeper brain structures or in the cerebellum. Therefore we also offer an option to use the entire brain volume as our source space (the green dots below represent dipoles locations in volume model). This produces results that can be better or worse depending on the data, but in all the cases much more difficult to review. Volume and mixed head volumes are discussed in the advanced tutorials about source modeling.
Forward problem
The first step of the source reconstruction consists in computing a model that explains how the electric currents or the magnetic fields flow from the electric generators in the brain (source space) through the different tissues of the head (mostly brain, CSF, skull and skin), to finally reach the sensors.
The question of building a model that connects the values we observe outside of the head (MEG/EEG) to the electric activity of the cortical dipoles in the brain is called forward problem.
The model we obtain after solving this problem is called head model in Brainstorm, but can also be referred to as forward model, leadfield matrix or gain matrix.
In this tutorial we will use the default source space: the low-resolution cortex surface with 15,000 vertices, as the support of 45,000 dipoles. We will use indifferently the terms dipole and source.
What we expect to get at the end of this process is a matrix [Nsensors x Nsources].
Available methods for MEG forward modeling
Single sphere: The head is considered as a homogeneous sphere.
Overlapping spheres: Refines the previous model by fitting one local sphere for each sensor.
OpenMEEG BEM: Symmetric Boundary Element Method from the open-source software OpenMEEG. Described in an advanced tutorial: BEM head model.
Models recommended for each modality
MEG: Overlapping spheres.
The magnetic fields are not affected too much by the heterogeneity of the tissues of the head. There is no real need for modeling the head with too much detail.EEG: OpenMEEG BEM.
The electric currents are strongly affected by jumps between very conductive tissues (brain, CSF, skin) and an isolant medium (the skull). A realistic head model is advised for integrating the properties of the skull correctly. When computing a BEM model is not an option, for instance if OpenMEEG crashes for unknown reasons, the Berg's three-layer sphere can be an acceptable option.sEEG/ECoG: The OpenMEEG BEM option is the only one available.
Computation
The forward models are related with the anatomy of the subject and the description of the sensors, therefore the menus associated to its computation are attached to the channel file.
In the imported Run#01, right-click on the channel file or the folder > Compute head model.
Keep the default options selected: Source space=Cortex, Forward model=Overlapping spheres.
You obtain one new file in the database. It is always saved in the same folder as the channel file.
There is not much you can do with this file except for using it for estimating sources. This will be the purpose of the following tutorials.Right-click on the new head model > Check spheres. This window shows the spheres that were estimated. You can check them by following the indications written in green at the bottom of the window: use left/right arrows. At each step, the current sensor marker is displayed in red, and the sphere you see is its local estimation of the inner skull shape.
This algorithm is supposed to use the inner skull surface from the subject, but we usually do not have this information. In this case, a pseudo-innerskull is reconstructed using a dilated version of the cortex envelope.
Repeat the same operation for the other file. We have two different acquisition runs with two different relative position of the head and the sensors, therefore we need to compute two different head models.
In the imported Run#02, right-click on the channel file > Compute head model.
Database explorer
Additional considerations about the management of the head model files.
If you have multiple head models computed in the same folder, you would see one displayed in green and the others in black. The one in green is selected as the default head model, it will be used for all the following computation steps. To change the default selection, double-click on another head model file (or right-click > Set as default head model).
You can use the database explore for batching the computation of the head model. The menu "Compute head model" is available in popup menus in the database explorer at all the levels. It is applied recursively to all the folders contained in the node(s) you selected.
On the hard drive
Right-click on any head model > File > View file contents:
Structure of the head model files: headmodel_*.mat
MEGMethod: Forward model used for MEG sensors ('os_meg', 'meg_sphere', 'openmeeg' or empty).
EEGMethod: Forward model used for EEG sensors ('eeg_3sphereberg', 'openmeeg' or empty).
ECOGMethod: Forward model used for ECoG sensors ('openmeeg' or empty).
SEEGMethod: Forward model used for sEEG sensors ('openmeeg' or empty).
Gain: Leadfield matrix, [Nsensors x Nsources], equivalent to [Nsensors x 3*Nvertices]
Comment: String displayed in the database explorer to represent this file.
HeadModelType: Type of source space used for this head model ('surface', 'volume', 'mixed').
GridLoc: [Nvertices x 3], (x,y,z) positions of the grid of source points. In the case of a surface head model, it corresponds to a copy of the 'Vertices' matrix from the cortex surface file.
GridOrient: [Nvertices x 3], direction of the normal to the surface for each vertex point (copy of the 'VertNormals' matrix of the cortex surface). Empty in the case of a volume head model.
GridAtlas: In the case of mixed head models, contains a copy of the "Source model options" atlas structure that was used for creating the model.
SurfaceFile: Relative path to the cortex surface file related with this head model.
Param: Description of the sphere that was estimated for each sensor (Center/Radius).
Gain matrix
The Gain matrix stores the leadfield for 3 orientations (x,y,z) at each grid point (p1, p2, ...).
The successive columns of the Gain matrix are: [p1_x, p1_y, p1_z, p2_x, p2_y, p2_z ...]To convert this unconstrained leadfield matrix to a constrained model, where the orientation of each dipole is fixed and normal to the cortex surface:
Export the head model file to the HeadModel structure: Right-click > File > Export to Matlab.
> Gain_constrained = bst_gain_orient(HeadModel.Gain, HeadModel.GridOrient);
The dimension of the output matrix is three times smaller: [Nsensors x Nvertices]
References
Huang MX, Mosher JC, Leahy RM (1999)
"A sensor-weighted overlapping-sphere head model and exhaustive head model comparison for MEG," Phys Med Biol, 44:423-440 | pdf
Additional documentation
Tutorial: BEM with OpenMEEG
Tutorial: Volume source estimation
External documentation: Electromagnetic neural source imaging
Forum: Sensor modeling: http://neuroimage.usc.edu/forums/showthread.php?1295
Forum: EEG reference: http://neuroimage.usc.edu/forums/showthread.php?1525#post6718
Forum: EEG and default anatomy: http://neuroimage.usc.edu/forums/showthread.php?1774
Forum: Mixed head models indices: http://neuroimage.usc.edu/forums/showthread.php?1878