Electrostatic models for multicompartment neuron models
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.
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),
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.
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
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 subclassing
CurrentDipoleMoment: Class for predicting current dipole moments
PointSourcePotential: Class for predicting extracellular potentials assuming point sources and point 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 sand outside a homogeneous sphere
LaminarCurrentSourceDensity: For computing the 'ground truth' current source density across cylindrical volumes aligned with the z-axis
VolumetricCurrentSourceDensity: 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
to extracellular measurements:
eegmegcalc.FourSphereVolumeConductor: For computing extracellular potentials in 4-sphere head model (brain, CSF, skull, scalp) from current dipole moment
eegmegcalc.InfiniteVolumeConductor: To compute extracellular potentials in infinite volume conductor from current dipole moment
eegmegcalc.MEG: Class for computing magnetic field from current dipole moments
eegmegcalc.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
that returns the linear map between the transmembrane currents or current dipole moment
and corresponding measurements (see Usage below)
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]])
Notes on physical units used in
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)
Transmembrane currents are represented by arrays with shape
n_segis the number of segments of the neuron model.
Current dipole moments are represented by arrays with shape
Response matrices M have shape
n_pointsis for instance the number of extracellular recording sites and
input.shapethe 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.MEG) have shape
The online Documentation of
LFPykit can be found here:
LFPykit is implemented in Python and is written (and continuously tested) for
Python >= 3.7.
LFPykit module depends on
MEAutility (https://github.com/alejoe91/MEAutility, https://meautility.readthedocs.io/en/latest/).
Running all unit tests and example files may in addition require
arbor coming) and
LFPy (https://github.com/LFPy/LFPy, https://LFPy.readthedocs.io).
From development sources (https://github.com/LFPy/LFPykit)
$ git clone https://github.com/LFPy/LFPykit.git $ cd LFPykit $ python setup.py install # --user optional
$ 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)
lfpykit from the
conda-forge channel can be achieved by adding
conda-forge to your channels with:
$ conda config --add channels conda-forge
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
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