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Electrostatic models for multicompartment neuron models

Project description

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:

  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

  3. 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

  4. Nunez and Srinivasan, Oxford University Press, 2006

  5. 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

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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 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 CurrentDipoleMoment) 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 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) where n_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]) where n_points is for instance the number of extracellular recording sites and input.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.MEG) 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

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