LFPykit 0.5.1
Electrostatic models for multicompartment neuron models
Requires Python: >=3.7

# 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.InfiniteHomogeneousVolCondMEG`:
  Class for computing magnetic field from current dipole moments under the assumption
  of infinite homogeneous volume conductor model
* `eegmegcalc.SphericallySymmetricVolCondMEG`:
  Class for computing magnetic field from current dipole moments under the assumption
  of a spherically symmetric volume conductor model
* `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.InfiniteHomogeneousVolCondMEG` or
  `eegmegcalc.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