Welcome to LFPykit’s documentation!
LFPykit
This Python module contain freestanding implementations of electrostatic forward models incorporated in LFPy (https://github.com/LFPy/LFPy, https://LFPy.readthedocs.io).
The aim of the LFPykit
module is to provide electrostatic models
in a manner that facilitates forward-model predictions of extracellular
potentials and related measures from multicompartment neuron models, but
without explicit dependencies on neural simulation software such as
NEURON (https://neuron.yale.edu, https://github.com/neuronsimulator/nrn),
Arbor (https://arbor.readthedocs.io, https://github.com/arbor-sim/arbor),
or even LFPy.
The LFPykit
module can then be more easily incorporated with
these simulators, or in various projects that utilize them such as
LFPy (https://LFPy.rtfd.io, https://github.com/LFPy/LFPy).
BMTK (https://alleninstitute.github.io/bmtk/, https://github.com/AllenInstitute/bmtk),
etc.
Its main functionality is providing class methods that return two-dimensional linear transformation matrices M between transmembrane currents I of multicompartment neuron models and some measurement Y given by Y=MI.
The presently incorporated volume conductor models have been incorporated in LFPy (https://LFPy.rtfd.io, https://github.com/LFPy/LFPy), as described in various papers and books:
Linden H, Hagen E, Leski S, Norheim ES, Pettersen KH, Einevoll GT (2014) LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Front. Neuroinform. 7:41. doi: 10.3389/fninf.2013.00041
Hagen E, Næss S, Ness TV and Einevoll GT (2018) Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0. Front. Neuroinform. 12:92. doi: 10.3389/fninf.2018.00092
Ness, T. V., Chintaluri, C., Potworowski, J., Leski, S., Glabska, H., Wójcik, D. K., et al. (2015). Modelling and analysis of electrical potentials recorded in microelectrode arrays (MEAs). Neuroinformatics 13:403–426. doi: 10.1007/s12021-015-9265-6
Nunez and Srinivasan, Oxford University Press, 2006
Næss S, Chintaluri C, Ness TV, Dale AM, Einevoll GT and Wójcik DK (2017). Corrected Four-sphere Head Model for EEG Signals. Front. Hum. Neurosci. 11:490. doi: 10.3389/fnhum.2017.00490
Build Status
Features
LFPykit
presently incorporates different electrostatic forward models for extracellular potentials
and magnetic signals that has been derived using volume conductor theory.
In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons.
Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed.
The module presently incorporates different classes. To represent the geometry of a multicompartment neuron model we have:
CellGeometry
: Base class representing a multicompartment neuron geometry in terms of segment x-, y-, z-coordinates and diameter.
Different classes built to map transmembrane currents of CellGeometry
like instances
to different measurement modalities:
LinearModel
: Base class representing a generic forward model for subclassingCurrentDipoleMoment
: Class for predicting current dipole momentsPointSourcePotential
: Class for predicting extracellular potentials assuming point sources and point contactsLineSourcePotential
: Class for predicting extracellular potentials assuming line sourcers and point contactsRecExtElectrode
: Class for simulations of extracellular potentialsRecMEAElectrode
: Class for simulations of in vitro (slice) extracellular potentialsOneSphereVolumeConductor
: For computing extracellular potentials within sand outside a homogeneous sphereLaminarCurrentSourceDensity
: For computing the ‘ground truth’ current source density across cylindrical volumes aligned with the z-axisVolumetricCurrentSourceDensity
: For computing the ‘ground truth’ current source density on regularly spaced 3D grid
Different classes built to map current dipole moments (i.e., computed using CurrentDipoleMoment
)
to extracellular measurements:
eegmegcalc.FourSphereVolumeConductor
: For computing extracellular potentials in 4-sphere head model (brain, CSF, skull, scalp) from current dipole momenteegmegcalc.InfiniteVolumeConductor
: To compute extracellular potentials in infinite volume conductor from current dipole momenteegmegcalc.InfiniteHomogeneousVolCondMEG
: Class for computing magnetic field from current dipole moments under the assumption of infinite homogeneous volume conductor modeleegmegcalc.SphericallySymmetricVolCondMEG
: Class for computing magnetic field from current dipole moments under the assumption of a spherically symmetric volume conductor modeleegmegcalc.NYHeadModel
: Class for computing extracellular potentials in detailed head volume conductor model (https://www.parralab.org/nyhead)
Each class (except CellGeometry
) should have a public method get_transformation_matrix()
that returns the linear map between the transmembrane currents or current dipole moment
and corresponding measurements (see Usage below)
Usage
A basic usage example using a mock 3-segment stick-like neuron, treating each segment as a point source in a linear, isotropic and homogeneous volume conductor, computing the extracellular potential in ten different locations alongside the cell geometry:
>>> # imports
>>> import numpy as np
>>> from lfpykit import CellGeometry, PointSourcePotential
>>> n_seg = 3
>>> # instantiate class `CellGeometry`:
>>> cell = CellGeometry(x=np.array([[0.] * 2] * n_seg), # (µm)
y=np.array([[0.] * 2] * n_seg), # (µm)
z=np.array([[10. * x, 10. * (x + 1)]
for x in range(n_seg)]), # (µm)
d=np.array([1.] * n_seg)) # (µm)
>>> # instantiate class `PointSourcePotential`:
>>> psp = PointSourcePotential(cell,
x=np.ones(10) * 10,
y=np.zeros(10),
z=np.arange(10) * 10,
sigma=0.3)
>>> # get linear response matrix mapping currents to measurements
>>> M = psp.get_transformation_matrix()
>>> # transmembrane currents (nA):
>>> imem = np.array([[-1., 1.],
[0., 0.],
[1., -1.]])
>>> # compute extracellular potentials (mV)
>>> V_ex = M @ imem
>>> V_ex
array([[-0.01387397, 0.01387397],
[-0.00901154, 0.00901154],
[ 0.00901154, -0.00901154],
[ 0.01387397, -0.01387397],
[ 0.00742668, -0.00742668],
[ 0.00409718, -0.00409718],
[ 0.00254212, -0.00254212],
[ 0.00172082, -0.00172082],
[ 0.00123933, -0.00123933],
[ 0.00093413, -0.00093413]])
A basic usage example using a mock 3-segment stick-like neuron, treating each segment as a point source, computing the current dipole moment and computing the potential in ten different remote locations away from the cell geometry:
>>> # imports
>>> import numpy as np
>>> from lfpykit import CellGeometry, CurrentDipoleMoment, \
>>> eegmegcalc
>>> n_seg = 3
>>> # instantiate class `CellGeometry`:
>>> cell = CellGeometry(x=np.array([[0.] * 2] * n_seg), # (µm)
y=np.array([[0.] * 2] * n_seg), # (µm)
z=np.array([[10. * x, 10. * (x + 1)]
for x in range(n_seg)]), # (µm)
d=np.array([1.] * n_seg)) # (µm)
>>> # instantiate class `CurrentDipoleMoment`:
>>> cdp = CurrentDipoleMoment(cell)
>>> M_I_to_P = cdp.get_transformation_matrix()
>>> # instantiate class `eegmegcalc.InfiniteVolumeConductor` and map dipole moment to
>>> # extracellular potential at measurement sites
>>> ivc = eegmegcalc.InfiniteVolumeConductor(sigma=0.3)
>>> # compute linear response matrix between dipole moment and
>>> # extracellular potential
>>> M_P_to_V = ivc.get_transformation_matrix(np.c_[np.ones(10) * 1000,
np.zeros(10),
np.arange(10) * 100])
>>> # transmembrane currents (nA):
>>> imem = np.array([[-1., 1.],
[0., 0.],
[1., -1.]])
>>> # compute extracellular potentials (mV)
>>> V_ex = M_P_to_V @ M_I_to_P @ imem
>>> V_ex
array([[ 0.00000000e+00, 0.00000000e+00],
[ 5.22657054e-07, -5.22657054e-07],
[ 1.00041193e-06, -1.00041193e-06],
[ 1.39855769e-06, -1.39855769e-06],
[ 1.69852477e-06, -1.69852477e-06],
[ 1.89803345e-06, -1.89803345e-06],
[ 2.00697409e-06, -2.00697409e-06],
[ 2.04182029e-06, -2.04182029e-06],
[ 2.02079888e-06, -2.02079888e-06],
[ 1.96075587e-06, -1.96075587e-06]])
Physical units
Notes on physical units used in LFPykit
:
There are no explicit checks for physical units
Transmembrane currents are assumed to be in units of (nA)
Spatial information is assumed to be in units of (µm)
Voltages are assumed to be in units of (mV)
Extracellular conductivities are assumed to be in units of (S/m)
current dipole moments are assumed to be in units of (nA µm)
Magnetic fields are assumed to be in units of (nA/µm)
Dimensionality
Transmembrane currents are represented by arrays with shape
(n_seg, n_timesteps)
wheren_seg
is the number of segments of the neuron model.Current dipole moments are represented by arrays with shape
(3, n_timesteps)
Response matrices M have shape
(n_points, input.shape[0])
wheren_points
is for instance the number of extracellular recording sites andinput.shape[0]
the first dimension of the input; that is, the number of segments in case of transmembrane currents or 3 in case of current dipole moments.predicted signals (except magnetic fields using
eegmegcalc.InfiniteHomogeneousVolCondMEG
oreegmegcalc.SphericallySymmetricVolCondMEG
) have shape(n_points, n_timesteps)
Documentation
The online Documentation of LFPykit
can be found here:
https://lfpykit.readthedocs.io/en/latest
Dependencies
LFPykit
is implemented in Python and is written (and continuously tested) for Python >= 3.7
.
The main LFPykit
module depends on numpy
, scipy
and MEAutility
(https://github.com/alejoe91/MEAutility, https://meautility.readthedocs.io/en/latest/).
Running all unit tests and example files may in addition require py.test
, matplotlib
,
neuron
(https://www.neuron.yale.edu),
(arbor
coming) and
LFPy
(https://github.com/LFPy/LFPy, https://LFPy.readthedocs.io).
Installation
From development sources (https://github.com/LFPy/LFPykit)
Install the current development version on https://GitHub.com using git
(https://git-scm.com):
$ git clone https://github.com/LFPy/LFPykit.git
$ cd LFPykit
$ python setup.py install # --user optional
or using pip
:
$ pip install . # --user optional
For active development, link the repository location
$ python setup.py develop # --user optional
Installation of stable releases on PyPI.org (https://www.pypi.org)
Installing from the Python Package Index (https://www.pypi.org/project/lfpykit):
$ pip install lfpykit # --user optional
To upgrade the installation using pip:
$ pip install --upgrade --no-deps lfpykit
Installation of stable releases on conda-forge (https://conda-forge.org)
Installing lfpykit
from the conda-forge
channel can be achieved by adding conda-forge
to your channels with:
$ conda config --add channels conda-forge
Once the conda-forge
channel has been enabled, lfpykit
can be installed with:
$ conda install lfpykit
It is possible to list all of the versions of lfpykit
available on your platform with:
$ conda search lfpykit --channel conda-forge
Module lfpykit
Initialization of LFPykit
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
- Classes
- CellGeometry:
Base class representing a multicompartment neuron geometry for subclassing
- LinearModel:
Base class representing a generic forward model for subclassing
- CurrentDipoleMoment:
Class for predicting current dipole moments
- PointSourcePotential:
Class for predicting extracellular potentials assuming point sources and contacts
- LineSourcePotential:
Class for predicting extracellular potentials assuming line sourcers and point contacts
- RecExtElectrode:
Class for simulations of extracellular potentials
- RecMEAElectrode:
Class for simulations of in vitro (slice) extracellular potentials
- OneSphereVolumeConductor:
For computing extracellular potentials within and outside a homogeneous sphere
- LaminarCurrentSourceDensity:
For computing the ground truth current source density in cylindrical volumes aligned with the z-axis.
- VolumetricCurrentSourceDensity:
For computing the ground truth current source density in cubic volumes with bin edges defined by x, y, z
- eegmegcalc.FourSphereVolumeConductor:
For computing extracellular potentials in 4-sphere model (brain, CSF, skull, scalp) from current dipole moment
- eegmegcalc.InfiniteVolumeConductor:
To compute extracellular potentials with current dipole moments in infinite volume conductor
- eegmegcalc.InfiniteHomogeneousVolCondMEG:
Class for computing magnetic field from current dipole moments assuming an infinite homogeneous volume conductor
- eegmegcalc.SphericallySymmetricVolCondMEG:
Class for computing magnetic field from current dipole moments assuming a spherically symmetric volume conductor
- eegmegcalc.NYHeadModel:
Class for computing extracellular potentials in detailed head volume conductor model (https://www.parralab.org/nyhead)
- Modules
cellgeometry
models
eegmegcalc
lfpcalc
class CellGeometry
- class lfpykit.CellGeometry(x, y, z, d)[source]
Bases:
object
Base class representing the geometry of multicompartment neuron models.
- Assumptions
each compartment is piecewise linear between their start and endpoints
each compartment has a constant diameter
the transmembrane current density is constant along the compartment axis
- Parameters
- x: ndarray of floats
shape (n_seg x 2) array of start- and end-point coordinates of each compartment along x-axis in units of (µm)
- y: ndarray
shape (n_seg x 2) array of start- and end-point coordinates of each compartment along y-axis in units of (µm)
- z: ndarray
shape (n_seg x 2) array of start- and end-point coordinates of each compartment along z-axis in units of (µm)
- d: ndarray
shape (n_seg) or shape (n_seg x 2) array of compartment diameters in units of (µm). If the 2nd axis is equal to 2, conical frusta is assumed.
- Attributes
- totnsegs: int
number of compartments
- x: ndarray of floats
shape (totnsegs x 2) array of start- and end-point coordinates of each compartment along x-axis in units of (µm)
- y: ndarray
shape (totnsegs x 2) array of start- and end-point coordinates of each compartment along y-axis in units of (µm)
- z: ndarray
shape (totnsegs x 2) array of start- and end-point coordinates of each compartment along z-axis in units of (µm)
- d: ndarray
shape (totnsegs) array of compartment diameters in units of (µm)
- length: ndarray
lenght of each compartment in units of um
- area: ndarray
array of compartment surface areas in units of um^2
Module lfpykit.models
Copyright (C) 2020 Computational Neuroscience Group, NMBU.
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
class LinearModel
- class lfpykit.LinearModel(cell)[source]
Bases:
lfpykit.models.Model
Base class that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane currents \(\mathbf{I}\) (nA) of a multicompartment neuron model and some measurement \(\mathbf{Y}\) as
\[\mathbf{Y} = \mathbf{M} \mathbf{I}\]LinearModel
only creates a mapping that returns the currents themselves. The class is suitable as a base class for other linear model implementations, see for example classCurrentDipoleMoment
orPointSourcePotential
- Parameters
- cell: object
lfpykit.CellGeometry
instance or similar. Can also be set toNone
which allows setting the attributecell
after class instantiation.
class CurrentDipoleMoment
- class lfpykit.CurrentDipoleMoment(cell)[source]
Bases:
lfpykit.models.LinearModel
LinearModel
subclass that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding current dipole moment \(\mathbf{P}\) (nA µm) [1] as\[\mathbf{P} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and the rows of \(\mathbf{P}\) represent the x-, y- and z-components of the current diple moment for every time step.
The current dipole moment can be used to compute distal measures of neural activity such as the EEG and MEG using
lfpykit.eegmegcalc.FourSphereVolumeConductor
orlfpykit.eegmegcalc.MEG
, respectively- Parameters
- cell: object
CellGeometry
instance or similar.
See also
References
- 1
H. Lindén, K. H. Pettersen, G. T. Einevoll (2010). Intrinsic dendritic filtering gives low-pass power spectra of local field potentials. J Comput Neurosci, 29:423–444. DOI: 10.1007/s10827-010-0245-4
Examples
Compute the current dipole moment of a 3-compartment neuron model:
>>> import numpy as np >>> from lfpykit import CellGeometry, CurrentDipoleMoment >>> n_seg = 3 >>> cell = CellGeometry(x=np.array([[0.]*2]*n_seg), y=np.array([[0.]*2]*n_seg), z=np.array([[1.*x, 1.*(x+1)] for x in range(n_seg)]), d=np.array([1.]*n_seg)) >>> cdm = CurrentDipoleMoment(cell) >>> M = cdm.get_transformation_matrix() >>> imem = np.array([[-1., 1.], [0., 0.], [1., -1.]]) >>> P = M@imem >>> P array([[ 0., 0.], [ 0., 0.], [ 2., -2.]])
class PointSourcePotential
- class lfpykit.PointSourcePotential(cell, x, y, z, sigma=0.3)[source]
Bases:
lfpykit.models.LinearModel
LinearModel
subclass that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding extracellular electric potential \(\mathbf{V}_{ex}\) (mV) as\[\mathbf{V}_{ex} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and each row indexed by \(j\) of \(\mathbf{V}_{ex}\) represents the electric potential at each measurement site for every time step.
The elements of \(\mathbf{M}\) are computed as
\[M_{ji} = 1 / (4 \pi \sigma |\mathbf{r}_i - \mathbf{r}_j|)\]where \(\sigma\) is the electric conductivity of the extracellular medium, \(\mathbf{r}_i\) the midpoint coordinate of segment \(i\) and \(\mathbf{r}_j\) the coordinate of measurement site \(j\) [1], [2].
Assumptions:
the extracellular conductivity \(\sigma\) is infinite, homogeneous, frequency independent (linear) and isotropic.
each segment is treated as a point source located at the midpoint between its start and end point coordinate.
each measurement site \(\mathbf{r}_j = (x_j, y_j, z_j)\) is treated as a point.
\(|\mathbf{r}_i - \mathbf{r}_j| >= d_i / 2\), where \(d_i\) is the segment diameter.
- Parameters
- cell: object
CellGeometry
instance or similar.- x: ndarray of floats
x-position of measurement sites (µm)
- y: ndarray of floats
y-position of measurement sites (µm)
- z: ndarray of floats
z-position of measurement sites (µm)
- sigma: float > 0
scalar extracellular conductivity (S/m)
References
- 1
Linden H, Hagen E, Leski S, Norheim ES, Pettersen KH, Einevoll GT (2014) LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Front. Neuroinform. 7:41. doi: 10.3389/fninf.2013.00041
- 2
Hagen E, Næss S, Ness TV and Einevoll GT (2018) Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0. Front. Neuroinform. 12:92. doi: 10.3389/fninf.2018.00092
Examples
Compute the current dipole moment of a 3-compartment neuron model:
>>> import numpy as np >>> from lfpykit import CellGeometry, PointSourcePotential >>> n_seg = 3 >>> cell = CellGeometry(x=np.array([[0.]*2]*n_seg), y=np.array([[0.]*2]*n_seg), z=np.array([[10.*x, 10.*(x+1)] for x in range(n_seg)]), d=np.array([1.]*n_seg)) >>> psp = PointSourcePotential(cell, x=np.ones(10)*10, y=np.zeros(10), z=np.arange(10)*10, sigma=0.3) >>> M = psp.get_transformation_matrix() >>> imem = np.array([[-1., 1.], [0., 0.], [1., -1.]]) >>> V_ex = M @ imem >>> V_ex array([[-0.01387397, 0.01387397], [-0.00901154, 0.00901154], [ 0.00901154, -0.00901154], [ 0.01387397, -0.01387397], [ 0.00742668, -0.00742668], [ 0.00409718, -0.00409718], [ 0.00254212, -0.00254212], [ 0.00172082, -0.00172082], [ 0.00123933, -0.00123933], [ 0.00093413, -0.00093413]])
class LineSourcePotential
- class lfpykit.LineSourcePotential(cell, x, y, z, sigma=0.3)[source]
Bases:
lfpykit.models.LinearModel
LinearModel
subclass that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding extracellular electric potential \(\mathbf{V}_{ex}\) (mV) as\[\mathbf{V}_{ex} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and each row indexed by \(j\) of \(\mathbf{V}_{ex}\) represents the electric potential at each measurement site for every time step.
The elements of \(\mathbf{M}\) are computed as
\[M_{ji} = \frac{1}{ 4 \pi \sigma L_i } \log \left| \frac{\sqrt{h_{ji}^2+r_{ji}^2}-h_{ji} }{ \sqrt{l_{ji}^2+r_{ji}^2}-l_{ji}} \right|\]Segment length is denoted \(L_i\), perpendicular distance from the electrode point contact to the axis of the line segment is denoted \(r_{ji}\), longitudinal distance measured from the start of the segment is denoted \(h_{ji}\), and longitudinal distance from the other end of the segment is denoted \(l_{ji}= L_i + h_{ji}\) [1], [2].
Assumptions:
the extracellular conductivity \(\sigma\) is infinite, homogeneous, frequency independent (linear) and isotropic
each segment is treated as a straight line source with homogeneous current density between its start and end point coordinate
each measurement site \(\mathbf{r}_j = (x_j, y_j, z_j)\) is treated as a point
The minimum distance to a line source is set equal to segment radius.
- Parameters
- cell: object
CellGeometry instance or similar.
- x: ndarray of floats
x-position of measurement sites (µm)
- y: ndarray of floats
y-position of measurement sites (µm)
- z: ndarray of floats
z-position of measurement sites (µm)
- sigma: float > 0
scalar extracellular conductivity (S/m)
References
- 1
Linden H, Hagen E, Leski S, Norheim ES, Pettersen KH, Einevoll GT (2014) LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Front. Neuroinform. 7:41. doi: 10.3389/fninf.2013.00041
- 2
Hagen E, Næss S, Ness TV and Einevoll GT (2018) Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0. Front. Neuroinform. 12:92. doi: 10.3389/fninf.2018.00092
Examples
Compute the current dipole moment of a 3-compartment neuron model:
>>> import numpy as np >>> from lfpykit import CellGeometry, LineSourcePotential >>> n_seg = 3 >>> cell = CellGeometry(x=np.array([[0.]*2]*n_seg), y=np.array([[0.]*2]*n_seg), z=np.array([[10.*x, 10.*(x+1)] for x in range(n_seg)]), d=np.array([1.]*n_seg)) >>> lsp = LineSourcePotential(cell, x=np.ones(10)*10, y=np.zeros(10), z=np.arange(10)*10, sigma=0.3) >>> M = lsp.get_transformation_matrix() >>> imem = np.array([[-1., 1.], [0., 0.], [1., -1.]]) >>> V_ex = M @ imem >>> V_ex array([[-0.01343699, 0.01343699], [-0.0084647 , 0.0084647 ], [ 0.0084647 , -0.0084647 ], [ 0.01343699, -0.01343699], [ 0.00758627, -0.00758627], [ 0.00416681, -0.00416681], [ 0.002571 , -0.002571 ], [ 0.00173439, -0.00173439], [ 0.00124645, -0.00124645], [ 0.0009382 , -0.0009382 ]])
class RecExtElectrode
- class lfpykit.RecExtElectrode(cell, sigma=0.3, probe=None, x=None, y=None, z=None, N=None, r=None, n=None, contact_shape='circle', method='linesource', verbose=False, seedvalue=None, **kwargs)[source]
Bases:
lfpykit.models.LinearModel
class RecExtElectrode
Main class that represents an extracellular electric recording devices such as a laminar probe.
This class is a
LinearModel
subclass that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding extracellular electric potential \(\mathbf{V}_{ex}\) (mV) as\[\mathbf{V}_{ex} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and each row indexed by \(j\) of \(\mathbf{V}_{ex}\) represents the electric potential at each measurement site for every time step.
The class differ from
PointSourcePotential
andLineSourcePotential
by:supporting anisotropic volume conductors [1]
supporting probe geometry specifications using
MEAutility
(https://meautility.readthedocs.io/en/latest/, https://github.com/alejoe91/MEAutility).supporting electrode contact points with finite extents [2], [3]
switching between point- and linesources, and a combined method that assumes that the root element at segment index 0 is spherical.
- Parameters
- cell: object
CellGeometry
instance or similar.- sigma: float or list/ndarray of floats
extracellular conductivity in units of (S/m). A scalar value implies an isotropic extracellular conductivity. If a length 3 list or array of floats is provided, these values corresponds to an anisotropic conductor with conductivities \([\sigma_x,\sigma_y,\sigma_z]\).
- probe: MEAutility MEA object or None
MEAutility probe object
- x, y, z: ndarray
coordinates or same length arrays of coordinates in units of (µm).
- N: None or list of lists
Normal vectors [x, y, z] of each circular electrode contact surface, default None
- r: float
radius of each contact surface, default None (µm)
- n: int
if N is not None and r > 0, the number of discrete points used to compute the n-point average potential on each circular contact point.
- contact_shape: str
‘circle’/’square’ (default ‘circle’) defines the contact point shape If ‘circle’ r is the radius, if ‘square’ r is the side length
- method: str
switch between the assumption of ‘linesource’, ‘pointsource’, ‘root_as_point’ to represent each compartment when computing extracellular potentials
- verbose: bool
Flag for verbose output, i.e., print more information
- seedvalue: int
random seed when finding random position on contact with r > 0
- **kwargs:
Additional keyword arguments parsed to RecExtElectrode.lfp_method() which is determined by method parameter.
References
- 1
Ness, T. V., Chintaluri, C., Potworowski, J., Leski, S., Glabska, H., Wójcik, D. K., et al. (2015). Modelling and analysis of electrical potentials recorded in microelectrode arrays (MEAs). Neuroinformatics 13:403–426. doi: 10.1007/s12021-015-9265-6
- 2
Linden H, Hagen E, Leski S, Norheim ES, Pettersen KH, Einevoll GT (2014) LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Front. Neuroinform. 7:41. doi: 10.3389/fninf.2013.00041
- 3
Hagen E, Næss S, Ness TV and Einevoll GT (2018) Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0. Front. Neuroinform. 12:92. doi: 10.3389/fninf.2018.00092
Examples
Mock cell geometry and transmembrane currents:
>>> import numpy as np >>> from lfpykit import CellGeometry, RecExtElectrode >>> # cell geometry with three segments (µm) >>> cell = CellGeometry(x=np.array([[0, 0], [0, 0], [0, 0]]), >>> y=np.array([[0, 0], [0, 0], [0, 0]]), >>> z=np.array([[0, 10], [10, 20], [20, 30]]), >>> d=np.array([1, 1, 1])) >>> # transmembrane currents, three time steps (nA) >>> I_m = np.array([[0., -1., 1.], [-1., 1., 0.], [1., 0., -1.]]) >>> # electrode locations (µm) >>> r = np.array([[28.24653166, 8.97563241, 18.9492774, 3.47296614, >>> 1.20517729, 9.59849603, 21.91956616, 29.84686727, >>> 4.41045505, 3.61146625], >>> [24.4954352, 24.04977922, 22.41262238, 10.09702942, >>> 3.28610789, 23.50277637, 8.14044367, 4.46909208, >>> 10.93270117, 24.94698813], >>> [19.16644585, 15.20196335, 18.08924828, 24.22864702, >>> 5.85216751, 14.8231048, 24.72666694, 17.77573431, >>> 29.34508292, 9.28381892]]) >>> # instantiate electrode, get linear response matrix >>> el = RecExtElectrode(cell=cell, x=r[0, ], y=r[1, ], z=r[2, ], >>> sigma=0.3, >>> method='pointsource') >>> M = el.get_transformation_matrix() >>> # compute extracellular potential >>> M @ I_m array([[-4.11657148e-05, 4.16621950e-04, -3.75456235e-04], [-6.79014892e-04, 7.30256301e-04, -5.12414088e-05], [-1.90930536e-04, 7.34007655e-04, -5.43077119e-04], [ 5.98270144e-03, 6.73490846e-03, -1.27176099e-02], [-1.34547752e-02, -4.65520036e-02, 6.00067788e-02], [-7.49957880e-04, 7.03763787e-04, 4.61940938e-05], [ 8.69330232e-04, 1.80346156e-03, -2.67279180e-03], [-2.04546513e-04, 6.58419628e-04, -4.53873115e-04], [ 6.82640209e-03, 4.47953560e-03, -1.13059377e-02], [-1.33289553e-03, -1.11818140e-04, 1.44471367e-03]])
Compute extracellular potentials after simulating and storage of transmembrane currents with the LFPy.Cell class:
>>> import os >>> import numpy as np >>> import matplotlib.pyplot as plt >>> import LFPy >>> from lfpykit import CellGeometry, RecExtElectrode >>> >>> cellParameters = { >>> 'morphology': os.path.join(LFPy.__path__[0], 'test', >>> 'ball_and_sticks.hoc'), >>> 'v_init': -65, # initial voltage >>> 'cm': 1.0, # membrane capacitance >>> 'Ra': 150, # axial resistivity >>> 'passive': True, # insert passive channels >>> 'passive_parameters': {"g_pas":1./3E4, >>> "e_pas":-65}, # passive params >>> 'dt': 2**-4, # simulation time res >>> 'tstart': 0., # start t of simulation >>> 'tstop': 50., # end t of simulation >>> } >>> cell = LFPy.Cell(**cellParameters) >>> >>> synapseParameters = { >>> 'idx': cell.get_closest_idx(x=0, y=0, z=800), # segment >>> 'e': 0, # reversal potential >>> 'syntype': 'ExpSyn', # synapse type >>> 'tau': 2, # syn. time constant >>> 'weight': 0.01, # syn. weight >>> 'record_current': True # syn. current record >>> } >>> synapse = LFPy.Synapse(cell, **synapseParameters) >>> synapse.set_spike_times(np.array([10., 15., 20., 25.])) >>> >>> cell.simulate(rec_imem=True) >>> >>> N = np.empty((16, 3)) >>> for i in range(N.shape[0]): N[i,] = [1, 0, 0] # normal vectors >>> electrodeParameters = { # parameters for RecExtElectrode class >>> 'sigma': 0.3, # Extracellular potential >>> 'x': np.zeros(16)+25, # Coordinates of electrode contacts >>> 'y': np.zeros(16), >>> 'z': np.linspace(-500,1000,16), >>> 'n': 20, >>> 'r': 10, >>> 'N': N, >>> } >>> electrode = RecExtElectrode(cell, **electrodeParameters) >>> M = electrode.get_transformation_matrix() >>> V_ex = M @ cell.imem >>> plt.matshow(V_ex) >>> plt.colorbar() >>> plt.axis('tight') >>> plt.show()
Compute extracellular potentials during simulation:
>>> import os >>> import numpy as np >>> import matplotlib.pyplot as plt >>> import LFPy >>> from lfpykit import CellGeometry, RecExtElectrode >>> >>> cellParameters = { >>> 'morphology': os.path.join(LFPy.__path__[0], 'test', >>> 'ball_and_sticks.hoc'), >>> 'v_init': -65, # initial voltage >>> 'cm': 1.0, # membrane capacitance >>> 'Ra': 150, # axial resistivity >>> 'passive': True, # insert passive channels >>> 'passive_parameters': {"g_pas":1./3E4, >>> "e_pas":-65}, # passive params >>> 'dt': 2**-4, # simulation time res >>> 'tstart': 0., # start t of simulation >>> 'tstop': 50., # end t of simulation >>> } >>> cell = LFPy.Cell(**cellParameters) >>> >>> synapseParameters = { >>> 'idx': cell.get_closest_idx(x=0, y=0, z=800), # compartment >>> 'e': 0, # reversal potential >>> 'syntype': 'ExpSyn', # synapse type >>> 'tau': 2, # syn. time constant >>> 'weight': 0.01, # syn. weight >>> 'record_current': True # syn. current record >>> } >>> synapse = LFPy.Synapse(cell, **synapseParameters) >>> synapse.set_spike_times(np.array([10., 15., 20., 25.])) >>> >>> N = np.empty((16, 3)) >>> for i in range(N.shape[0]): N[i,] = [1, 0, 0] #normal vec. of contacts >>> electrodeParameters = { # parameters for RecExtElectrode class >>> 'sigma': 0.3, # Extracellular potential >>> 'x': np.zeros(16)+25, # Coordinates of electrode contacts >>> 'y': np.zeros(16), >>> 'z': np.linspace(-500,1000,16), >>> 'n': 20, >>> 'r': 10, >>> 'N': N, >>> } >>> electrode = RecExtElectrode(cell, **electrodeParameters) >>> cell.simulate(probes=[electrode]) >>> plt.matshow(electrode.data) >>> plt.colorbar() >>> plt.axis('tight') >>> plt.show()
Use MEAutility to to handle probes
>>> import os >>> import numpy as np >>> import matplotlib.pyplot as plt >>> import MEAutility as mu >>> import LFPy >>> from lfpykit import CellGeometry, RecExtElectrode >>> >>> cellParameters = { >>> 'morphology': os.path.join(LFPy.__path__[0], 'test', >>> 'ball_and_sticks.hoc'), >>> 'v_init': -65, # initial voltage >>> 'cm': 1.0, # membrane capacitance >>> 'Ra': 150, # axial resistivity >>> 'passive': True, # insert passive channels >>> 'passive_parameters': {"g_pas":1./3E4, >>> "e_pas":-65}, # passive params >>> 'dt': 2**-4, # simulation time res >>> 'tstart': 0., # start t of simulation >>> 'tstop': 50., # end t of simulation >>> } >>> cell = LFPy.Cell(**cellParameters) >>> >>> synapseParameters = { >>> 'idx': cell.get_closest_idx(x=0, y=0, z=800), # compartment >>> 'e': 0, # reversal potential >>> 'syntype': 'ExpSyn', # synapse type >>> 'tau': 2, # syn. time constant >>> 'weight': 0.01, # syn. weight >>> 'record_current': True # syn. current record >>> } >>> synapse = LFPy.Synapse(cell, **synapseParameters) >>> synapse.set_spike_times(np.array([10., 15., 20., 25.])) >>> >>> cell.simulate(rec_imem=True) >>> >>> probe = mu.return_mea('Neuropixels-128') >>> electrode = RecExtElectrode(cell, probe=probe) >>> V_ex = electrode.get_transformation_matrix() @ cell.imem >>> mu.plot_mea_recording(V_ex, probe) >>> plt.axis('tight') >>> plt.show()
class RecMEAElectrode
- class lfpykit.RecMEAElectrode(cell, sigma_T=0.3, sigma_S=1.5, sigma_G=0.0, h=300.0, z_shift=0.0, steps=20, probe=None, x=array([0]), y=array([0]), z=array([0]), N=None, r=None, n=None, method='linesource', verbose=False, seedvalue=None, squeeze_cell_factor=None, **kwargs)[source]
Bases:
lfpykit.models.RecExtElectrode
class RecMEAElectrode
Electrode class that represents an extracellular in vitro slice recording as a Microelectrode Array (MEA). Inherits RecExtElectrode class
Illustration:
Above neural tissue (Saline) -> sigma_S <----------------------------------------------------> z = z_shift + h Neural Tissue -> sigma_T o -> source_pos = [x',y',z'] <-----------*----------------------------------------> z = z_shift + 0 \-> elec_pos = [x,y,z] Below neural tissue (MEA Glass plate) -> sigma_G
For further details, see reference [1].
- Parameters
- cell: object
GeometryCell instance or similar.
- sigma_T: float
extracellular conductivity of neural tissue in unit (S/m)
- sigma_S: float
conductivity of saline bath that the neural slice is immersed in [1.5] (S/m)
- sigma_G: float
conductivity of MEA glass electrode plate. Most commonly assumed non-conducting [0.0] (S/m)
- h: float, int
Thickness in um of neural tissue layer containing current the current sources (i.e., in vitro slice or cortex)
- z_shift: float, int
Height in um of neural tissue layer bottom. If e.g., top of neural tissue layer should be z=0, use z_shift=-h. Defaults to z_shift = 0, so that the neural tissue layer extends from z=0 to z=h.
- squeeze_cell_factor: float or None
Factor to squeeze the cell in the z-direction. This is needed for large cells that are thicker than the slice, since no part of the cell is allowed to be outside the slice. The squeeze is done after the neural simulation, and therefore does not affect neuronal simulation, only calculation of extracellular potentials.
- probe: MEAutility MEA object or None
MEAutility probe object
- x, y, z: np.ndarray
coordinates or arrays of coordinates in units of (um). Must be same length
- N: None or list of lists
Normal vectors [x, y, z] of each circular electrode contact surface, default None
- r: float
radius of each contact surface, default None
- n: int
if N is not None and r > 0, the number of discrete points used to compute the n-point average potential on each circular contact point.
- contact_shape: str
‘circle’/’square’ (default ‘circle’) defines the contact point shape If ‘circle’ r is the radius, if ‘square’ r is the side length
- method: str
switch between the assumption of ‘linesource’, ‘pointsource’, ‘root_as_point’ to represent each compartment when computing extracellular potentials
- verbose: bool
Flag for verbose output, i.e., print more information
- seedvalue: int
random seed when finding random position on contact with r > 0
References
- 1
Ness, T. V., Chintaluri, C., Potworowski, J., Leski, S., Glabska, H., Wójcik, D. K., et al. (2015). Modelling and analysis of electrical potentials recorded in microelectrode arrays (MEAs). Neuroinformatics 13:403–426. doi: 10.1007/s12021-015-9265-6
Examples
Mock cell geometry and transmembrane currents:
>>> import numpy as np >>> from lfpykit import CellGeometry, RecMEAElectrode >>> # cell geometry with four segments (µm) >>> cell = CellGeometry( >>> x=np.array([[0, 10], [10, 20], [20, 30], [30, 40]]), >>> y=np.array([[0, 0], [0, 0], [0, 0], [0, 0]]), >>> z=np.array([[0, 0], [0, 0], [0, 0], [0, 0]]) + 10, >>> d=np.array([1, 1, 1, 1])) >>> # transmembrane currents, three time steps (nA) >>> I_m = np.array([[0.25, -1., 1.], >>> [-1., 1., -0.25], >>> [1., -0.25, -1.], >>> [-0.25, 0.25, 0.25]]) >>> # electrode locations (µm) >>> r = np.stack([np.arange(10)*4 + 2, np.zeros(10), np.zeros(10)]) >>> # instantiate electrode, get linear response matrix >>> el = RecMEAElectrode(cell=cell, >>> sigma_T=0.3, sigma_S=1.5, sigma_G=0.0, >>> x=r[0, ], y=r[1, ], z=r[2, ], >>> method='pointsource') >>> M = el.get_transformation_matrix() >>> # compute extracellular potential >>> M @ I_m array([[-0.00233572, -0.01990957, 0.02542055], [-0.00585075, -0.01520865, 0.02254483], [-0.01108601, -0.00243107, 0.01108601], [-0.01294584, 0.01013595, -0.00374823], [-0.00599067, 0.01432711, -0.01709416], [ 0.00599067, 0.01194602, -0.0266944 ], [ 0.01294584, 0.00953841, -0.02904238], [ 0.01108601, 0.00972426, -0.02324134], [ 0.00585075, 0.01075236, -0.01511768], [ 0.00233572, 0.01038382, -0.00954429]])
See also <LFPy>/examples/example_MEA.py
>>> import os >>> import numpy as np >>> import matplotlib.pyplot as plt >>> import LFPy >>> from lfpykit import CellGeometry, RecMEAElectrode >>> >>> cellParameters = { >>> 'morphology': os.path.join(LFPy.__path__[0], 'test', >>> 'ball_and_sticks.hoc'), >>> 'v_init': -65, # initial voltage >>> 'cm': 1.0, # membrane capacitance >>> 'Ra': 150, # axial resistivity >>> 'passive': True, # insert passive channels >>> 'passive_parameters': {"g_pas":1./3E4, >>> "e_pas":-65}, # passive params >>> 'dt': 2**-4, # simulation time res >>> 'tstart': 0., # start t of simulation >>> 'tstop': 50., # end t of simulation >>> } >>> cell = LFPy.Cell(**cellParameters) >>> cell.set_rotation(x=np.pi/2, z=np.pi/2) >>> cell.set_pos(z=100) >>> synapseParameters = { >>> 'idx': cell.get_closest_idx(x=800, y=0, z=100), # segment >>> 'e': 0, # reversal potential >>> 'syntype': 'ExpSyn', # synapse type >>> 'tau': 2, # syn. time constant >>> 'weight': 0.01, # syn. weight >>> 'record_current': True # syn. current record >>> } >>> synapse = LFPy.Synapse(cell, **synapseParameters) >>> synapse.set_spike_times(np.array([10., 15., 20., 25.])) >>> >>> MEA_electrode_parameters = { >>> 'sigma_T': 0.3, # extracellular conductivity >>> 'sigma_G': 0.0, # MEA glass electrode plate conductivity >>> 'sigma_S': 1.5, # Saline bath conductivity >>> 'x': np.linspace(0, 1200, 16), # 1d vector of positions >>> 'y': np.zeros(16), >>> 'z': np.zeros(16), >>> "method": "pointsource", >>> "h": 300, >>> "squeeze_cell_factor": 0.5, >>> } >>> cell.simulate(rec_imem=True) >>> >>> MEA = RecMEAElectrode(cell, **MEA_electrode_parameters) >>> V_ext = MEA.get_transformation_matrix() @ lfpy_cell.imem >>> >>> plt.matshow(V_ext) >>> plt.colorbar() >>> plt.axis('tight') >>> plt.show()
- distort_cell_geometry(axis='z', nu=0.0)[source]
Distorts cellular morphology with a relative squeeze_cell_factor along a chosen axis preserving Poisson’s ratio. A ratio nu=0.5 assumes uncompressible and isotropic media that embeds the cell. A ratio nu=0 will only affect geometry along the chosen axis. A ratio nu=-1 will isometrically scale the neuron geometry along each axis. This method does not affect the underlying cable properties of the cell, only predictions of extracellular measurements (by affecting the relative locations of sources representing the compartments).
- Parameters
- axis: str
which axis to apply compression/stretching. Default is “z”.
- nu: float
Poisson’s ratio. Ratio between axial and transversal compression/stretching. Default is 0.
class OneSphereVolumeConductor
- class lfpykit.OneSphereVolumeConductor(cell, r, R=10000.0, sigma_i=0.3, sigma_o=0.03)[source]
Bases:
lfpykit.models.LinearModel
Computes extracellular potentials within and outside a spherical volume- conductor model that assumes homogeneous, isotropic, linear (frequency independent) conductivity in and outside the sphere with a radius R. The conductivity in and outside the sphere must be greater than 0, and the current source(s) must be located within the radius R.
The implementation is based on the description of electric potentials of point charge in an dielectric sphere embedded in dielectric media [1], which is mathematically equivalent to a current source in conductive media.
This class is a
LinearModel
subclass that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding extracellular electric potential \(\mathbf{V}_{ex}\) (mV) as\[\mathbf{V}_{ex} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and each row indexed by \(j\) of \(\mathbf{V}_{ex}\) represents the electric potential at each measurement site for every time step.
- Parameters
- cell: object or None
CellGeometry
instance or similar.- r: ndarray, dtype=float
shape(3, n_points) observation points in space in spherical coordinates (radius, theta, phi) relative to the center of the sphere.
- R: float
sphere radius (µm)
- sigma_i: float
electric conductivity for radius r <= R (S/m)
- sigma_o: float
electric conductivity for radius r > R (S/m)
References
- 1
Shaozhong Deng (2008), Journal of Electrostatics 66:549-560. DOI: 10.1016/j.elstat.2008.06.003
Examples
Compute the potential for a single monopole along the x-axis:
>>> # import modules >>> from lfpykit import OneSphereVolumeConductor >>> import numpy as np >>> import matplotlib.pyplot as plt >>> # observation points in spherical coordinates (flattened) >>> X, Y = np.mgrid[-15000:15100:1000., -15000:15100:1000.] >>> r = np.array([np.sqrt(X**2 + Y**2).flatten(), >>> np.arctan2(Y, X).flatten(), >>> np.zeros(X.size)]) >>> # set up class object and compute electric potential in all locations >>> sphere = OneSphereVolumeConductor(cell=None, r=r, R=10000., >>> sigma_i=0.3, sigma_o=0.03) >>> Phi = sphere.calc_potential(rs=8000, current=1.).reshape(X.shape) >>> # plot >>> fig, ax = plt.subplots(1,1) >>> im=ax.contourf(X, Y, Phi, >>> levels=np.linspace(Phi.min(), >>> np.median(Phi[np.isfinite(Phi)]) * 4, 30)) >>> circle = plt.Circle(xy=(0,0), radius=sphere.R, fc='none', ec='k') >>> ax.add_patch(circle) >>> fig.colorbar(im, ax=ax) >>> plt.show()
- calc_potential(rs, current, min_distance=1.0, n_max=1000)[source]
Return the electric potential at observation points for source current as function of time.
- Parameters
- rs: float
monopole source location along the horizontal x-axis (µm)
- current: float or ndarray, dtype float
float or shape (n_tsteps, ) array containing source current (nA)
- min_distance: None or float
minimum distance between source location and observation point (µm) (in order to avoid singularities)
- n_max: int
Number of elements in polynomial expansion to sum over (see [1]).
- Returns
- Phi: ndarray
shape (n-points, ) ndarray of floats if I is float like. If I is an 1D ndarray, and shape (n-points, I.size) ndarray is returned. Unit (mV).
References
- 1
Shaozhong Deng (2008), Journal of Electrostatics 66:549-560. DOI: 10.1016/j.elstat.2008.06.003
- get_transformation_matrix(n_max=1000)[source]
Compute linear mapping between transmembrane currents of
CellGeometry
like object instance and extracellular potential in and outside of sphere.- Parameters
- n_max: int
Number of elements in polynomial expansion to sum over (see [1]).
- Returns
- ndarray
Shape (n_points, n_compartments) mapping between individual segments and extracellular potential in extracellular locations
- Raises
- AttributeError
if
cell is None
Notes
Each segment is treated as a point source in space. The minimum source to measurement site distance will be set to the diameter of each segment
References
- 1
Shaozhong Deng (2008), Journal of Electrostatics 66:549-560. DOI: 10.1016/j.elstat.2008.06.003
Examples
Compute extracellular potential in one-sphere volume conductor model from
LFPy.Cell
object:>>> # import modules >>> import LFPy >>> from lfpykit import CellGeometry, >>> OneSphereVolumeConductor >>> import os >>> import numpy as np >>> import matplotlib.pyplot as plt >>> from matplotlib.collections import PolyCollection >>> # create cell >>> cell = LFPy.Cell(morphology=os.path.join(LFPy.__path__[0], 'test', >>> 'ball_and_sticks.hoc'), >>> tstop=10.) >>> cell.set_pos(z=9800.) >>> # stimulus >>> syn = LFPy.Synapse(cell, idx=cell.totnsegs-1, syntype='Exp2Syn', >>> weight=0.01) >>> syn.set_spike_times(np.array([1.])) >>> # simulate >>> cell.simulate(rec_imem=True) >>> # observation points in spherical coordinates (flattened) >>> X, Z = np.mgrid[-500:501:10., 9500:10501:10.] >>> Y = np.zeros(X.shape) >>> r = np.array([np.sqrt(X**2 + Z**2).flatten(), >>> np.arccos(Z / np.sqrt(X**2 + Z**2)).flatten(), >>> np.arctan2(Y, X).flatten()]) >>> # set up class object and compute mapping between segment currents >>> # and electric potential in space >>> sphere = OneSphereVolumeConductor(cell, r=r, R=10000., >>> sigma_i=0.3, sigma_o=0.03) >>> M = sphere.get_transformation_matrix(n_max=1000) >>> # pick out some time index for the potential and compute potential >>> ind = cell.tvec==2. >>> V_ex = (M @ cell.imem)[:, ind].reshape(X.shape) >>> # plot potential >>> fig, ax = plt.subplots(1,1) >>> zips = [] >>> for x, z in cell.get_idx_polygons(projection=('x', 'z')): >>> zips.append(list(zip(x, z))) >>> polycol = PolyCollection(zips, >>> edgecolors='none', >>> facecolors='gray') >>> vrange = 1E-3 # limits for color contour plot >>> im=ax.contour(X, Z, V_ex, >>> levels=np.linspace(-vrange, vrange, 41)) >>> circle = plt.Circle(xy=(0,0), radius=sphere.R, fc='none', ec='k') >>> ax.add_collection(polycol) >>> ax.add_patch(circle) >>> ax.axis(ax.axis('equal')) >>> ax.set_xlim(X.min(), X.max()) >>> ax.set_ylim(Z.min(), Z.max()) >>> fig.colorbar(im, ax=ax) >>> plt.show()
class LaminarCurrentSourceDensity
- class lfpykit.LaminarCurrentSourceDensity(cell, z, r)[source]
Bases:
lfpykit.models.LinearModel
Facilitates calculations of the ground truth Current Source Density (CSD) in cylindrical volumes aligned with the z-axis based on [1] and [2].
The implementation assumes piecewise linear current sources similar to
LineSourcePotential
, and accounts for the fraction of each segment’s length within each volume, see Eq. 11 in [2].This class is a
LinearModel
subclass that defines a 2D linear response matrix \(\mathbf{M}\) between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding CSD \(\mathbf{C}\) (nA/µm^3) as\[\mathbf{C} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and each row indexed by \(j\) of \(\mathbf{C}\) represents the CSD in each volume for every time step as the sum of currents divided by the volume.
- Parameters
- cell: object or None
CellGeometry
instance or similar.- z: ndarray, dtype=float
shape (n_volumes, 2) array of lower and upper edges of each volume along the z-axis in units of (µm). The lower edge value must be below the upper edge value.
- r: ndarray, dtype=float
shape (n_volumes, ) array with assumed radius of each cylindrical volume. Each radius must be greater than zero, and in units of (µm)
- Raises
- AttributeError
inputs
z
andr
must be ndarrays of correct shape etc.
References
- 1
Pettersen KH, Hagen E, Einevoll GT (2008) Estimation of population firing rates and current source densities from laminar electrode recordings. J Comput Neurosci (2008) 24:291–313. DOI 10.1007/s10827-007-0056-4
- 2
Hagen E, Fossum JC, Pettersen KH, Alonso JM, Swadlow HA, Einevoll GT (2017) Journal of Neuroscience, 37(20):5123-5143. DOI: https://doi.org/10.1523/JNEUROSCI.2715-16.2017
Examples
Mock cell geometry and transmembrane currents:
>>> import numpy as np >>> from lfpykit import CellGeometry, LaminarCurrentSourceDensity >>> # cell geometry with three segments (µm) >>> cell = CellGeometry(x=np.array([[0, 0], [0, 0], [0, 0]]), >>> y=np.array([[0, 0], [0, 0], [0, 0]]), >>> z=np.array([[0, 10], [10, 20], [20, 30]]), >>> d=np.array([1, 1, 1])) >>> # transmembrane currents, three time steps (nA) >>> I_m = np.array([[0., -1., 1.], [-1., 1., 0.], [1., 0., -1.]]) >>> # define geometry (z - upper and lower boundary; r - radius) >>> # of cylindrical volumes aligned with the z-axis (µm) >>> z = np.array([[-10., 0.], [0., 10.], [10., 20.], >>> [20., 30.], [30., 40.]]) >>> r = np.array([100., 100., 100., 100., 100.]) >>> # instantiate electrode, get linear response matrix >>> csd = LaminarCurrentSourceDensity(cell=cell, z=z, r=r) >>> M = csd.get_transformation_matrix() >>> # compute current source density [nA/µm3] >>> M @ I_m array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [ 0.00000000e+00, -3.18309886e-06, 3.18309886e-06], [-3.18309886e-06, 3.18309886e-06, 0.00000000e+00], [ 3.18309886e-06, 0.00000000e+00, -3.18309886e-06], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]])
class VolumetricCurrentSourceDensity
- class lfpykit.VolumetricCurrentSourceDensity(cell, x=None, y=None, z=None, dl=1.0)[source]
Bases:
lfpykit.models.LinearModel
Facilitates calculations of the ground truth Current Source Density (CSD) across 3D volumetric grid with bin edges defined by parameters
x
,y
andz
.The implementation assumes piecewise constant current sources similar to
LineSourcePotential
, and accounts for the fraction of each segment’s length within each volume by counting the number of points representing partial segments with max lengthdl
divided by the number of partial segments.This class is a
LinearModel
subclass that defines a 4D linear response matrix \(\mathbf{M}\) of shape(x.size-1, y.size-1, z.size-1, n_seg)
between transmembrane current array \(\mathbf{I}\) (nA) of a multicompartment neuron model and the corresponding CSD \(\mathbf{C}\) (nA/µm^3) as\[\mathbf{C} = \mathbf{M} \mathbf{I}\]The current \(\mathbf{I}\) is an ndarray of shape (n_seg, n_tsteps) with unit (nA), and each row indexed by \(j\) of \(\mathbf{C}\) represents the CSD in each bin for every time step as the sum of currents divided by the volume.
- Parameters
- cell: object or None
CellGeometry
instance or similar.- x, y, z: ndarray, dtype=float
shape (n, ) array of bin edges of each volume along each axis in units of (µm). Must be monotonously increasing.
- dl: float
discretization length of compartments before binning (µm). Default=1. Lower values will result in more accurate estimates as each line source gets split into more points.
- Raises
See also
Notes
The resulting mapping M may be very sparse (i.e, mostly made up by zeros) and can be converted into a sparse array for more efficient multiplication for the same result:
>>> import scipy.sparse as ss >>> M_csc = ss.csc_matrix(M.reshape((-1, M.shape[-1]))) >>> C = M_csc @ I_m >>> np.all(C.reshape((M.shape[:-1] + (-1,))) == (M @ I_m)) True
Examples
Mock cell geometry and transmembrane currents:
>>> import numpy as np >>> from lfpykit import CellGeometry, VolumetricCurrentSourceDensity >>> # cell geometry with three segments (µm) >>> cell = CellGeometry(x=np.array([[0, 0], [0, 0], [0, 0]]), >>> y=np.array([[0, 0], [0, 0], [0, 0]]), >>> z=np.array([[0, 10], [10, 20], [20, 30]]), >>> d=np.array([1, 1, 1])) >>> # transmembrane currents, three time steps (nA) >>> I_m = np.array([[0., -1., 1.], [-1., 1., 0.], [1., 0., -1.]]) >>> # instantiate probe, get linear response matrix >>> csd = VolumetricCurrentSourceDensity(cell=cell, >>> x=np.linspace(-20, 20, 5), >>> y=np.linspace(-20, 20, 5), >>> z=np.linspace(-20, 20, 5), dl=1.) >>> M = csd.get_transformation_matrix() >>> # compute current source density [nA/µm3] >>> M @ I_m array([[[[ 0., 0., 0.], [ 0., 0., 0.], [ 0., 0., 0.], [ 0., 0., 0.]], ...
Module lfpykit.eegmegcalc
Collection of classes defining forward models applicable with current dipole moment predictions.
Copyright (C) 2017 Computational Neuroscience Group, NMBU. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
class eegmegcalc.FourSphereVolumeConductor
- class lfpykit.eegmegcalc.FourSphereVolumeConductor(r_electrodes, radii=[79000.0, 80000.0, 85000.0, 90000.0], sigmas=[0.3, 1.5, 0.015, 0.3], iter_factor=2.0202020202020204e-08)[source]
Bases:
lfpykit.eegmegcalc.Model
Main class for computing extracellular potentials in a four-sphere volume conductor model that assumes homogeneous, isotropic, linear (frequency independent) conductivity within the inner sphere and outer shells. The conductance outside the outer shell is 0 (air).
This class implements the corrected 4-sphere model described in [1], [2]
- Parameters
- r_electrodes: ndarray, dtype=float
Shape (n_contacts, 3) array containing n_contacts electrode locations in cartesian coordinates in units of (µm). All
r_el
inr_electrodes
must be less than or equal to scalp radius and larger than the distance between dipole and sphere center:|rz| < r_el <= radii[3]
.- radii: list, dtype=float
Len 4 list with the outer radii in units of (µm) for the 4 concentric shells in the four-sphere model: brain, csf, skull and scalp, respectively.
- sigmas: list, dtype=float
Len 4 list with the electrical conductivity in units of (S/m) of the four shells in the four-sphere model: brain, csf, skull and scalp, respectively.
- iter_factor: float
iteration-stop factor
See also
References
- 1
Næss S, Chintaluri C, Ness TV, Dale AM, Einevoll GT and Wójcik DK (2017) Corrected Four-sphere Head Model for EEG Signals. Front. Hum. Neurosci. 11:490. doi: 10.3389/fnhum.2017.00490
- 2
Hagen E, Næss S, Ness TV and Einevoll GT (2018) Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0. Front. Neuroinform. 12:92. doi: 10.3389/fninf.2018.00092
Examples
Compute extracellular potential from current dipole moment in four-sphere head model:
>>> from lfpykit.eegmegcalc import FourSphereVolumeConductor >>> import numpy as np >>> radii = [79000., 80000., 85000., 90000.] # (µm) >>> sigmas = [0.3, 1.5, 0.015, 0.3] # (S/m) >>> r_electrodes = np.array([[0., 0., 90000.], [0., 85000., 0.]]) # (µm) >>> sphere_model = FourSphereVolumeConductor(r_electrodes, radii, >>> sigmas) >>> # current dipole moment >>> p = np.array([[10.]*10, [10.]*10, [10.]*10]) # 10 timesteps (nA µm) >>> dipole_location = np.array([0., 0., 78000.]) # (µm) >>> # compute potential >>> sphere_model.get_dipole_potential(p, dipole_location) # (mV) array([[1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08, 1.06247669e-08], [2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10, 2.39290752e-10]])
- get_dipole_potential(p, dipole_location)[source]
Return electric potential from current dipole moment
p
in locationdipole_location
in locationsr_electrodes
- Parameters
- p: ndarray, dtype=float
Shape (3, n_timesteps) array containing the x,y,z components of the current dipole moment in units of (nA*µm) for all timesteps.
- dipole_location: ndarray, dtype=float
Shape (3, ) array containing the position of the current dipole in cartesian coordinates. Units of (µm).
- Returns
- potential: ndarray, dtype=float
Shape
(n_contacts, n_timesteps)
array containing the electric potential at contact point(s)FourSphereVolumeConductor.rxyz
in units of (mV) for all timesteps of current dipole momentp
.
- get_transformation_matrix(dipole_location)[source]
Get linear response matrix mapping current dipole moment in (nA µm) located in location
rz
to extracellular potential in (mV) at recording sitesFourSphereVolumeConductor.rxyz
(µm)- Parameters
- dipole_location: ndarray, dtype=float
Shape (3, ) array containing the position of the current dipole in cartesian coordinates. Units of (µm).
- Returns
- response_matrix: ndarray
shape (n_contacts, 3) ndarray
class eegmegcalc.InfiniteVolumeConductor
- class lfpykit.eegmegcalc.InfiniteVolumeConductor(sigma=0.3)[source]
Bases:
lfpykit.eegmegcalc.Model
Main class for computing extracellular potentials with current dipole moment \(\mathbf{P}\) in an infinite 3D volume conductor model that assumes homogeneous, isotropic, linear (frequency independent) conductivity \(\sigma\). The potential \(V\) is computed as [1]:
\[V = \frac{\mathbf{P} \cdot \mathbf{r}}{4 \pi \sigma r^3}\]- Parameters
- sigma: float
Electrical conductivity in extracellular space in units of (S/cm)
See also
References
- 1
Nunez and Srinivasan, Oxford University Press, 2006
Examples
Computing the potential from dipole moment valid in the far field limit.
>>> from lfpykit.eegmegcalc import InfiniteVolumeConductor >>> import numpy as np >>> inf_model = InfiniteVolumeConductor(sigma=0.3) >>> p = np.array([[10.], [10.], [10.]]) # (nA µm) >>> r = np.array([[1000., 0., 5000.]]) # (µm) >>> inf_model.get_dipole_potential(p, r) # (mV) array([[1.20049432e-07]])
- get_dipole_potential(p, r)[source]
Return electric potential from current dipole moment
p
in locationsr
relative to dipole- Parameters
- p: ndarray, dtype=float
Shape (3, n_timesteps) array containing the x,y,z components of the current dipole moment in units of (nA*µm) for all timesteps
- r: ndarray, dtype=float
Shape (n_contacts, 3) array containing the displacement vectors from dipole location to measurement location
- Returns
- potential: ndarray, dtype=float
Shape (n_contacts, n_timesteps) array containing the electric potential at contact point(s)
r
in units of (mV) for all timesteps of current dipole moment p
- get_transformation_matrix(r)[source]
Get linear response matrix mapping current dipole moment in (nA µm) to extracellular potential in (mV) at recording sites r (µm)
- Parameters
- r: ndarray, dtype=float
Shape (n_contacts, 3) array contaning the displacement vectors from dipole location to measurement location (µm)
- Returns
- response_matrix: ndarray
shape (n_contacts, 3) ndarray
class eegmegcalc.InfiniteHomogeneousVolCondMEG
- class lfpykit.eegmegcalc.InfiniteHomogeneousVolCondMEG(sensor_locations, mu=1.2566370614359173e-06)[source]
Bases:
lfpykit.eegmegcalc.Model
Basic class for computing magnetic field from current dipole moment in an infinite homogeneous volume conductor model. For this purpose we use the Biot-Savart law derived from Maxwell’s equations under the assumption of negligible magnetic induction effects [1]:
\[\mathbf{H} = \frac{\mathbf{p} \times \mathbf{R}}{4 \pi R^3}\]where \(\mathbf{p}\) is the current dipole moment, \(\mathbf{R}\) the vector between dipole source location and measurement location, and \(R=|\mathbf{R}|\)
Note that the magnetic field \(\mathbf{H}\) is related to the magnetic field \(\mathbf{B}\) as
\[\mu_0 \mathbf{H} = \mathbf{B}-\mathbf{M}\]where \(\mu_0\) is the permeability of free space (very close to permebility of biological tissues). \(\mathbf{M}\) denotes material magnetization (also ignored)
- Parameters
- sensor_locations: ndarray, dtype=float
shape (n_locations x 3) array with x,y,z-locations of measurement devices where magnetic field of current dipole moments is calculated. In unit of (µm)
- mu: float
Permeability. Default is permeability of vacuum (\(\mu_0 = 4*\pi*10^{-7}\) T*m/A)
- Raises
- AssertionError
If dimensionality of sensor_locations is wrong
References
- 1
Nunez and Srinivasan, Oxford University Press, 2006
Examples
Define cell object, create synapse, compute current dipole moment:
>>> import LFPy, os, numpy as np, matplotlib.pyplot as plt >>> from lfpykit import CurrentDipoleMoment >>> from lfpykit.eegmegcalc import InfiniteHomogeneousVolCondMEG as MEG >>> # create LFPy.Cell object >>> cell = LFPy.Cell(morphology=os.path.join(LFPy.__path__[0], 'test', >>> 'ball_and_sticks.hoc'), >>> passive=True) >>> cell.set_pos(0., 0., 0.) >>> # create single synaptic stimuli at soma (idx=0) >>> syn = LFPy.Synapse(cell, idx=0, syntype='ExpSyn', weight=0.01, tau=5, >>> record_current=True) >>> syn.set_spike_times_w_netstim() >>> # simulate, record current dipole moment >>> cell.simulate(rec_imem=True) >>> # Compute current dipole moment >>> cdp = CurrentDipoleMoment(cell=cell) >>> M_cdp = cdp.get_transformation_matrix() >>> current_dipole_moment = M_cdp @ cell.imem >>> # Compute the dipole location as an average of segment locations >>> # weighted by membrane area: >>> dipole_location = (cell.area * np.c_[cell.x.mean(axis=-1), >>> cell.y.mean(axis=-1), >>> cell.z.mean(axis=-1)].T >>> / cell.area.sum()).sum(axis=1) >>> # Define sensor site, instantiate MEG object, get transformation matrix >>> sensor_locations = np.array([[1E4, 0, 0]]) >>> meg = MEG(sensor_locations) >>> M = meg.get_transformation_matrix(dipole_location) >>> # compute the magnetic signal in a single sensor location: >>> H = M @ current_dipole_moment >>> # plot output >>> plt.figure(figsize=(12, 8), dpi=120) >>> plt.subplot(311) >>> plt.plot(cell.tvec, cell.somav) >>> plt.ylabel(r'$V_{soma}$ (mV)') >>> plt.subplot(312) >>> plt.plot(cell.tvec, syn.i) >>> plt.ylabel(r'$I_{syn}$ (nA)') >>> plt.subplot(313) >>> plt.plot(cell.tvec, H[0].T) >>> plt.ylabel(r'$H$ (nA/um)') >>> plt.xlabel('$t$ (ms)') >>> plt.legend(['$H_x$', '$H_y$', '$H_z$']) >>> plt.show()
- calculate_B(p, r_p)[source]
Compute magnetic field B from single current dipole
p
localized somewhere in space atr_p
.This function returns the magnetic field \(\mathbf{B}=µ\mathbf{H}\).
- Parameters
- p: ndarray, dtype=float
shape (3, n_timesteps) array with x,y,z-components of current- dipole moment time series data in units of (nA µm)
- r_p: ndarray, dtype=float
shape (3, ) array with x,y,z-location of dipole in units of (µm)
- Returns
- ndarray, dtype=float
shape (n_locations x 3 x n_timesteps) array with x,y,z-components of the magnetic field \(\mathbf{B}\) in units of (nA/µm)
- calculate_H(current_dipole_moment, dipole_location)[source]
Compute magnetic field H from single current-dipole moment localized in an infinite homogeneous volume conductor.
- Parameters
- current_dipole_moment: ndarray, dtype=float
shape (3, n_timesteps) array with x,y,z-components of current- dipole moment time series data in units of (nA µm)
- dipole_location: ndarray, dtype=float
shape (3, ) array with x,y,z-location of dipole in units of (µm)
- Returns
- ndarray, dtype=float
shape (n_locations x 3 x n_timesteps) array with x,y,z-components of the magnetic field \(\mathbf{H}\) in units of (nA/µm)
- Raises
- AssertionError
If dimensionality of current_dipole_moment and/or dipole_location is wrong
- get_transformation_matrix(dipole_location)[source]
Get linear response matrix mapping current dipole moment in (nA µm) located in location
dipole_location
to magnetic field \(\mathbf{H}\) in units of (nA/µm) atsensor_locations
- Parameters
- dipole_location: ndarray, dtype=float
shape (3, ) array with x,y,z-location of dipole in units of (µm)
- Returns
- response_matrix: ndarray
shape (n_contacts, 3, 3) ndarray
class eegmegcalc.SphericallySymmetricVolCondMEG
- class lfpykit.eegmegcalc.SphericallySymmetricVolCondMEG(r, mu=1.2566370614359173e-06)[source]
Bases:
lfpykit.eegmegcalc.Model
Computes magnetic fields from current dipole in spherically-symmetric volume conductor models.
This class facilitates calculations according to eq. (34) from [1] (see also [2]) defined as:
\[ \begin{align}\begin{aligned}\mathbf{H} = \frac{1}{4 \pi} \frac{F \mathbf{p} \times \mathbf{r}_p - (\mathbf{p} \times \mathbf{r}_p \cdot \mathbf{r}) \nabla F}{F^2}, \text{ where}\\F = a(ra + r^2 - \mathbf{r}_p \cdot \mathbf{r}),\\\nabla F = (r^{-1}a^2 + a^{-1}\mathbf{a} \cdot \mathbf{r} + 2a + 2r)\mathbf{r} -(a + 2r + a^{-1}\mathbf{a} \cdot \mathbf{r})\mathbf{r}_p,\\\mathbf{a} = \mathbf{r} - \mathbf{r}_p,\\a = |\mathbf{a}|,\\r = |\mathbf{r}| .\end{aligned}\end{align} \]Here, \(\mathbf{p}\) is the current dipole moment, \(\mathbf{r}\) the measurement location(s) and \(\mathbf{r}_p\) the current dipole location.
Note that the magnetic field \(\mathbf{H}\) is related to the magnetic field \(\mathbf{B}\) as
\[\mu_0 \mathbf{H} = \mathbf{B}-\mathbf{M} ,\]where \(\mu_0\) denotes the permeability of free space (very close to permebility of biological tissues). \(\mathbf{M}\) denotes material magnetization (which is ignored).
- Parameters
- r: ndarray
sensor locations, shape
(n, 3)
wheren
denotes number of locations, unit [µm]- mu: float
Permeability. Default is permeability of vacuum (\(\mu_0 = 4\pi 10^{-7}\) Tm/A)
- Raises
- AssertionError
If dimensionality of sensor locations
r
is wrong
See also
References
- 1
Hämäläinen M., et al., Reviews of Modern Physics, Vol. 65, No. 2, April 1993.
- 2
Sarvas J., Phys.Med. Biol., 1987, Vol. 32, No 1, 11-22.
Examples
Compute the magnetic field from a current dipole located
>>> import numpy as np >>> from lfpykit.eegmegcalc import SphericallySymmetricVolCondMEG >>> p = np.array([[0, 1, 0]]).T # tangential current dipole (nAµm) >>> r_p = np.array([0, 0, 90000]) # dipole location (µm) >>> r = np.array([[0, 0, 92000]]) # measurement location (µm) >>> m = SphericallySymmetricVolCondMEG(r=r) >>> M = m.get_transformation_matrix(r_p=r_p) >>> H = M @ p >>> H # magnetic field (nA/µm) array([[[9.73094081e-09], [0.00000000e+00], [0.00000000e+00]]])
- calculate_B(p, r_p)[source]
Compute magnetic field B from single current dipole
p
localized somewhere in space atr_p
.This function returns the magnetic field \(\mathbf{B}=µ\mathbf{H}\).
- Parameters
- p: ndarray, dtype=float
shape (3, n_timesteps) array with x,y,z-components of current- dipole moment time series data in units of (nA µm)
- r_p: ndarray, dtype=float
shape (3, ) array with x,y,z-location of dipole in units of (µm)
- Returns
- ndarray, dtype=float
shape (n_locations x 3 x n_timesteps) array with x,y,z-components of the magnetic field \(\mathbf{B}\) in units of (nA/µm)
- calculate_H(p, r_p)[source]
Compute magnetic field \(\mathbf{H}\) from single current dipole
p
localized somewhere in space atr_p
- Parameters
- p: ndarray, dtype=float
shape (3, n_timesteps) array with x,y,z-components of current- dipole moment time series data in units of (nA µm)
- r_p: ndarray, dtype=float
shape (3, ) array with x,y,z-location of dipole in units of (µm)
- Returns
- ndarray, dtype=float
shape (n_locations x 3 x n_timesteps) array with x,y,z-components of the magnetic field \(\mathbf{H}\) in units of (nA/µm)
- Raises
- AssertionError
If dimensionality of current_dipole_moment
p
and/or dipole_locationr_p
is wrong
- get_transformation_matrix(r_p)[source]
Get linear response matrix mapping current dipole moment in (nA µm) located in location
r_p
to magnetic field \(\mathbf{H}\) in units of (nA/µm) at sensor locationsr
- Parameters
- r_p: ndarray, dtype=float
shape (3, ) array with x,y,z-location of dipole in units of (µm)
- Returns
- response_matrix: ndarray
shape (n_sensors, 3, 3) ndarray
- Raises
- AssertionError
If dipole location
r_p
has the wrong shape or if its radius is greater than radius to any sensor location in<object>.r
class eegmegcalc.NYHeadModel
- class lfpykit.eegmegcalc.NYHeadModel(nyhead_file=None)[source]
Bases:
lfpykit.eegmegcalc.Model
Main class for computing EEG signals from current dipole moment \(\mathbf{P}\) in New York Head Model [1], [2]
Assumes units of nA * um for current dipole moment, and mV for the EEG
- Parameters
- nyhead_file: str [optional]
Location of file containing New York Head Model. If empty (or None), it will be looked for in the main LFPykit folder. If not present the user is asked if it should be downloaded from https://www.parralab.org/nyhead/sa_nyhead.mat
See also
Notes
The original unit of the New York model current dipole moment is (probably?) mA*m, and the EEG output unit is V. LFPykit’s current dipole moments have units nA*um, and EEGs from the NYhead model is here recomputed in units of mV.
References
- 1
Huang, Parra, Haufe (2016) The New York Head—A precise standardized volume conductor model for EEG source localization and tES targeting. Neuroimage 140:150–162. doi: 10.1016/j.neuroimage.2015.12.019
- 2
Naess et al. (2020) Biophysical modeling of the neural origin of EEG and MEG signals. bioRxiv 2020.07.01.181875. doi: 10.1101/2020.07.01.181875
Examples
Computing EEG from dipole moment.
>>> from lfpykit.eegmegcalc import NYHeadModel
>>> nyhead = NYHeadModel()
>>> nyhead.set_dipole_pos('parietal_lobe') # predefined example location >>> M = nyhead.get_transformation_matrix()
>>> # Rotate to be along normal vector of cortex >>> p = nyhead.rotate_dipole_to_surface_normal([[0.], [0.], [1.]]) >>> eeg = M @ p # (mV)
- find_closest_electrode()[source]
Returns minimal distance (mm) and closest electrode idx to dipole location specified in self.dipole_pos.
- get_transformation_matrix()[source]
Get linear response matrix mapping from current dipole moment (nA µm) to EEG signal (mV) at EEG electrodes (n=231)
- Returns
- response_matrix: ndarray
shape (231, 3) ndarray
- return_closest_idx(pos)[source]
Returns the index of the closest vertex in the brain to a given position (in mm).
- Parameters
- posarray of length (3)
[x, y, z] of a location in the brain, given in mm, and not in um which is the default position unit in LFPy
- Returns
- ——-
- idxint
Index of the vertex in the brain that is closest to the given location
- rotate_dipole_to_surface_normal(p, orig_ax_vec=[0, 0, 1])[source]
Returns rotated dipole moment, p_rot, oriented along the normal vector of the cortex at the dipole location
- Parameters
- pnp.ndarray of size (3, num_timesteps)
Current dipole moment from neural simulation, [p_x(t), p_y(t), p_z(t)]. If z-axis is the depth axis of cortex in the original neural simulation p_x(t) and p_y(t) will typically be small, and orig_ax_vec = [0, 0, 1].
- orig_ax_vecnp.ndarray or list of length (3)
Original surface vector of cortex in the neural simulation. If depth axis of cortex is the z-axis, orig_ax_vec = [0, 0, 1].
- Returns
- p_rotnp.ndarray of size (3, num_timesteps)
Rotated current dipole moment, oriented along cortex normal vector at the dipole location
References
See: https://en.wikipedia.org/wiki/Rotation_matrix under “Rotation matrix from axis and angle”
- set_dipole_pos(dipole_pos=None)[source]
Sets the dipole location in the brain
- Parameters
- dipole_pos: None, str or array of length (3) [x, y, z) (mm)
Location of the dipole. If no argument is given (or dipole_pos=None), a location, ‘motorsensory_cortex’, from self.dipole_pos_dict is used. If dipole_pos is an array of length 3, the closest vertex in the brain will be set as the dipole location.